abc Conjecture - Numberphile

The abc Conjecture may have been proven by a Japanese mathematician - but what is it?
More links & stuff in full description below ↓↓↓
Feeling brave and want to read the papers by Shinichi Mochizuki - www.kurims.kyoto-u.ac.jp/~moti... (scroll to the bottom)
This video features Dr James Grime who tweets at / jamesgrime
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[@pieguy159]

Pieguy159's conjecture: Whenever you use a marker, you will always end up writing on yourself.

[@chronos3783]

pieguy159 not always

[@dirtbikersteve]

ismartroman gamer you must not user markers

[@pieguy159]

I swear their skillz at not writing on theirselves while marker writing is tremendous

[@aliriano15]

awindwaker Fermat?

[@jackwalsh8601]

I have a truly marvellous proof of that statement but this KZbin comment is two small to contain it

[@marlenedietrich2468]

to those interested: the paper didn't get accepted as a proof edit: based on the replies, it seems that it may have been revisited. So I can't say what the status on it is

[@Kebabrulle4869]

Apel Pie Thanks for answering my question! This came up in my recommended again after 6 years and I wanted to know really badly how it went

[@blueberry1c2]

the poor dude wrote 500 pages :( i feel sorry for him

[@kielbarry1789]

Came here to request an update - this was the top answer. Thanks!

[@cube2fox]

There is an article by Quanta Magazine. Two German mathematicians claim to have found a serious mistake in the proof. Mochizuki has denied this. He wrote a rebuttal, saying that they didn't understand the proof. (I think the fact that the paper hasn't yet been accepted for publication isn't related to this.)

[@thesmart4128]

I thought it still wasn't decided.

[@aliebadi180]

I have discovered a truly marvelous proof of the abc conjecture which my brain is too small to contain.

[@NoriMori1992]

Best twist on the joke so far. Thumbs up.

[@titan1235813]

+NoriMori Ditto.

[@leofreitas4134]

I see what you did there

[@Lighthammer18]

Cuius rei demonstrationem mirabilem sane detexi hanc meum cerebri exiguitas non caperet.

[@roydadancegod]

Well the speculative proof is 500 pages long so ...

[@SimplyMyAccount]

At 0:51 when Brady accidentally shows the mannequin and then has to show the whole thing so its not weird that theres a face in the frame

[@badmanjones179]

nice catch haha

[@jasonwalker4610]

Ty Wood Yeah but why is it in his room?

[@cameodamaneo]

That's so subtle! I didn't even notice tbh!

[@shack8110]

what were they doing in his bedroom?

[@markbordelon1601]

@@shack8110 at least he remembered to move the mannequin out of the bed before filming

[@MewPurPur]

To those interested: a 600-page redo of the proof is gonna be published in a peer-reviewed journal. But it's still not accepted as a proof and even more controversy among mathematicians is going on now.

[@reddmst]

Gee, wonder why. Every sane mathematician on the planet: posts 10 papers, 10-50 pages long, in one-year delays, so that the community can dissect them, find mistakes or decide if it's correct, all in their own precious time, learning the new concepts introduced by the author step by step. Meanwhile, Shinichi Mochizuki: dumps 500 pages of cryptic gibberish at once, like "hey there, I heard you've got nothing to do for the next decade of your life, so here, learn an entire new branch of mathematics that I've been inventing in secret".

[@roelin360]

Isn't he also head of that journal? Sounds pretty shady to me

[@TheLukeLsd]

@@reddmst It's a convenient distraction.

[@hexagonist23]

Life is too short for these things.

[@singingbanana]

Fermat was almost certainly mistaken. It can happen to anyone - for example my mistake in this video!

[@ultraviolet.catastrophe]

What mistake? Anyway, don't beat up yourself too hard about it.

[@balaramkrishnahanumanthu5869]

Well wicked! 4:06

[@thepaperpilot3577]

Can you make a 1 hour version of well wicked

[@SatyarthShankar]

2*3*5*13*17=6630

[@Gelfling66]

"it's called the radical because it is well wicked" omfg im in tears

[@NoriMori1992]

What does "well wicked" even mean? I know what "wicked" means, but I've never heard the phrase "well wicked". In standard dialect that doesn't even make grammatical sense. XD

[@PavelFerst]

or "wickled"?

[@scottgoodson8295]

NoriMori It's a reference to Ali G, a character played by British comedian Sacha Baren Cohen.

[@harriehausenman8623]

@@scottgoodson8295 esp. the movie "Ali G Indahouse"

[@fenryrtheshaman]

@@scottgoodson8295 I think it and Ali G Indahouse are both references to UK jungle culture because M Beat by General Levy, song featured in in Ali G Indahouse when they're driving int he car, goes "Wicked Wicked Junglist Massive" and I've seen many other references in UK media to jungle culture

[@ronaldderooij1774]

1+2=3. Seems legit.

[@abdullahenaya]

Ronald de Rooij what do you mean by 1+2=3?

[@dnshist]

It follows the rules where the none of the terms share factors.

[@bailes0180]

Every who;e number shares the factor 1

[@Nandovisky]

Bailey Charter but then this problem is impossible, all numbers share the factor 1

[@bailes0180]

Canal do Saito I must've been really tired when I commented, I honestly have no idea where my logic was at

[@singingbanana]

If abc is true then there is an argument that shows there are no examples of x^n + y^ = z^n, if x and y are whole numbers and don't share any factors. That's nearly Fermat's Last Theorem, but the full version isn't restricted to whole numbers etc.

[@Sir_Isaac_Newton_]

first comment and squid game pfp. deal with it

[@nikhilnagaria2672]

Second comment on a 9y old comment by super nice person :D

[@speedstyle.]

Doesn't that imply FLT? If some counterexample 𝑥,𝑦,𝑧 had a common factor between 𝑥 and 𝑦, then 𝑧 would also be divisible by that factor, and you could make a new equation 𝑝ⁿ + 𝑞ⁿ = 𝑟ⁿ without those factors. So proving there's no coprime examples proves there's none at all, like with proofs of irrationality

[@dansanger5340]

I have discovered a truly marvelous proof of the abc conjecture that is too large to fit in a KZbin comment. I'll publish it when I have the time.

[@hecko-yes]

KZbin comments have no character limit. *fail*

[@FindusGame11]

+ToCzegoSzukasz No, you're the one who failed... lol

[@VolkColopatrion]

+Dan Sanger i have discovered a proof that information can be infinitely compressible. but it is much to small to fit in a youtube comme- Oh dear.

[@DanDart]

*dies* oops sorry

[@Scarlet.225]

Fermat is that you

[@gdogvibes1]

Even something this simple needs a 500 page explanation... Amazing how such simple questions have such complicated answers.

[@ITKinq]

***** The meaning of life is to be lived. If you dig deep inside this statement, you'll have your meaning of life.

[@hellterminator]

***** That won't work. Ever since the 1.8 snapshots /give only works with ID names (minecraft:wooden_door in this case) which will correctly resolve to the item ID for door as opposed to the block ID.

[@wewladstbh]

42

[@wewladstbh]

That's not what I was referencing.

[@dvada18]

***** Wow, you're so random and cool, I wish I could be as random as you

[@ThorHC11]

Funnily enough, Mochizuki's proof is still being checked to this day.

[@MrCheeze]

And now it's considered to be mistaken by most experts, though Mochizuki continues to maintain that they misunderstood his definitions.

[@vpambs1pt]

⁠@@MrCheezeyuup, from what I've seen it hasn't been accepted. Mainly because there are a few parts, where Mochizuki and some of his colleagues state that some propositions and statements are obvious and true, While the mathematicians who are reading it to understand, such as Peter Scholze, state the opposite, there is no foundation on those propositions, and they aren't obvious at all unlike Mochizuki says. Mochizuki didn't enter in much details to explain it, leaving some spaces in blank. So the big theorems are explained, it's that it's lacking some explanation that hasn't made sense by itself that the author and colleagues don't explain further. Wow even though there are some gaps, and pride, constructing a whole new mathematical theory is something else... Really admirable ^^ Parson me if there are some mistakes in the story, but it goes along these lines as far a is recall

[@jeelianbb6405]

@@vpambs1pt the proof is left as exercise to the reader

[@numberphile]

Some of out have quite correctly pointed out (to James' horror) that 2*3*5*13*17=6630, not 13260 The explanation still stands, this error withstanding.

[@numberphile]

There's a good explanation, but I'll leave it as a mystery for a bit longer!

[@Matthew-zy5sr]

hmm

[@pi4313]

What explanation

[@TehKhronicler]

IT'S WELL WICKED

[@diegoconnolly5317]

Why would you bother repeating something we all just watched?

[@MolotowCocktail24]

@@diegoconnolly5317 BECAUSE ITS WELL WICKED

[@redpepper74]

Diego Connolly Turn on subtitles to find out

[@guillermolangle]

Diego Connolly it’s censored in the closed captions. “It is [INAUDIBLE]”

[@ExplosiveBrohoof]

4:07 isn't inaudible. He said that "it's called the radical because it is well wicked."

[@lovexbibi]

hehehehe

[@jnazor]

This guy is such an underground raver.

[@deifiedtitan]

I think that's the joke. They've written "inaudible" because it was him being daft/cringe-worthy.

[@a.krueger6486]

Random terraform functions

[@cube2fox]

What does "well wicked" mean?

[@woodfur00]

I love the way his eyes light up when he's talking about how big this could be if it's proven. Dr. Grime's passion for maths really rubs off in his videos in a way that even other Numberphile speakers just can't match. He makes you want to learn it, and I love that.

[@heyitsalex99]

I WANT MORE NUMBERPHILE VIDEOS LIKE THIS, THEY WERE THE BEST

[@3vimages471]

a + b = c! Yes! At last a Numberphile I might actually understand .... or so I thought!

[@General12th]

a + b = c factorial... I wonder if there's some math secrets to be had there.

[@htmlguy88]

basically take a, b, and c be whole numbers such that a+b=c and a b and c share no factors, and let the radical equal the product of the prime factors of a, b, and c. given the above the radical of a*b*c to any power k>1 is greater than c with only finitely many exceptions . edited multiple times.

[@humanobject0.129]

@@General12th i was about to say it hahaha

[@darkseid856]

But 1+2 ≠ 3!

[@s.h5187]

I could finally understand what the meaning of thin conjecture is. As always your explanation is really easy to grasp.

[@MTd2]

The proof is so hard that after 3 and 1/2 years after the proof was announced, the method is not understood yet!

[@dalailamabama]

There is probably no proof. Mochizuki is perhaps new Langan.

[@pokeman123451]

SSS S Hopefully not. That would mean this guy in Japan doesn’t even really know maths. 👀

[@livinghooman8471]

@@dalailamabama Nah, the 'proof' Mochizuki has doesn't apply every time and there are some gaps according to most mathematicians, but the fact that there are gaps instead of the whole conjecture being flawed is already a step closer to a proof, or so I think.

[@hamiltonianpathondodecahed5236]

it has been 7 years now

[@soupisfornoobs4081]

@@hamiltonianpathondodecahed5236 make that 8

[@numberphile]

We'll get the full 500 pages into the next one maybe? Basically the Japnese guy proved the conjecture explained throughout this video. The details of his proof is well beyond our powers!

[@Siberian_Khatru.]

Damn i am the first person to like this comment after 10 years!

[@enryu5191]

@@Siberian_Khatru. damn

[@KAJlogic]

​@@jamescharles5907unproven still

[@Celestia1323]

​@@Siberian_Khatru. damn

[@TonyChan1986]

1 man come up with the prove, 8 years to be accepted. AMAZING

[@mathphysicsnerd]

You think that's long, read up on the Flyspeck project some time

[@dangiscongrataway2365]

I just browsed the papers, how can people be so geniuses, I'm jealous :/

[@delilahwood3708]

I'm always so glad to get an email saying there is a new Numberphile video! Vihart introduced me to you guys several months ago, and I was amazed at how much math there really was that I hadn't got the chance to learn yet! I spent SOOOOOO many hours trying to catch up, and I still haven't caught all the way up yet. Every time I watch your videos I feel like you're my teacher/friend; it's so great! I LOVE MATH SO MUCH, and I'm so glad you guys do this for people like me; a math lover!-ObsessedFan

[@ROCCOANDROXY]

The conjecture basically states the following: Definition: For any positive integer n the radical of n denoted by rad(n) is the product of distinct prime factors of n. For example rad(12) = rad(2^2 * 3) = 2 * 3 = 6. Let a,b,and c be positive integers. If gcf(a,b,c) = 1 such that a + b = c, then it is usually the case that rad(a * b * c) > c so the abc conjecture deals with the exceptions. Now, to state the conjecture. For every epsilon > 0 there exists only a finite number of triples (a,b,c) with gcf(a,b,c) = 1 and a + b = c such that c > rad(a * b * c)^(1 + epsilon). Let a = 12 = 2^2 * 3 b = 11 c = a + b = 23 and rad(a * b * c) = 2 * 3 * 11 * 23 > c which is the usual case. The power (1 + epsilon) is necessary since there are an infinite triples (a.b.c) with gcf(a,b,c) = 1 and a + b = c such that c > rad(a * b * c). For example: a = 1 b = 2^(6 * n) - 1, where n is a positive integer c = 2^(6 * n) Show: 9|b For n = 1 we have b = 63 = 7 * 9 --> 9|b Assume 9|b for some positive integer n > 1 --> 2^(6 * n) - 1 = 9 * j. Show 9|(2^(6 * (n + 1)) - 1) 2^(6 * (n + 1)) - 1 = 2^(6 * n + 6) - 1 = 2^(6 * n) * 2^6 - 1 = (9 * j + 1) * 2^6 - 1 = 2^6 * 9 * j + 2^ 6 - 1 = 2^6 * 9 * j + 63 = 9 * (2^6 * j + 7) = 9 * k --> 9|(2^(6 * (n + 1)) - 1) By mathematical induction 9|b for all positive integers n. Now rad(b) = rad(3^2 * j) = 3 * j = b/3 and rad(c) = 2 --> rad(a * b * c) = 2 * rad(b) = 2 * b/3 < 2 * c/3 < c. If anyone is interested I wrote a short program(using free pascal) that generates some of the above triples satisfying the abc conjecture. program test; {for abc conjecture} uses mathunit; var testabc:text; procedure abc; var a,b,c,prod,j:longint; const last1 = 50; last2 = 5000; last3 = 30; begin assign(testabc,'abc.txt'); rewrite(testabc); for a:= 1 to last1 do begin for b:= a + 1 to last2 do begin c:= a + b; if gcf(gcf(a,b),c) = 1 then begin prod:= rad(a) * rad(b) * rad(c); for j:= 2 to last3 do {abc conjecture} begin if c > power(nroot(prod,j),j + 1) then writeln(testabc, 'c = ', c, ' > rad(a * b * c))^', j + 1,'/',j,' = ',power(nroot(prod,j),j + 1):0:9, ' where a = ', a, ' b = ',b); end; end; end; end; close(testabc); end; begin abc; readln; end. The functions used above where in my unit mathunit. You can make a unit for them or use them directly in the above program. function prime(p:integer):boolean; var n:integer; begin{prime} if p = 1 then prime:= false else if p = 2 then prime:= true else begin{else} prime:= true; n:=2; while (n < trunc(sqrt(p)) + 1) do begin{loop} if p mod n = 0 then prime:= false; n:= n + 1; end;{loop} end{else} end;{prime} function gcf(m,k:LONGINT):LONGINT; {lcm calls gcf ---> need longint} var n,factor,min:INTEGER; begin{gcf} if m = 1) THEN BEGIN left:= 1; right:= ABS(x); END; IF (ABS(X) < 1) THEN BEGIN LEFT:= ABS(X); RIGHT:= 1; END; midpt:= (left + right)/2; count:= 1; repeat if power(midpt,n) > ABS(x) then {X CAN < 0 FOR N ODD} right:= midpt {ASSUMES X >= 0 FOR N EVEN} else {ALWAYS USE SAFEGUARD FOR N EVEN} left:= midpt; count:= count + 1; midpt:= (left + right)/2; diff:= abs(ABS(x) - power(midpt,n)); until((diff < error) or (count = 100)); IF (X < 0) AND (N MOD 2 = 1) THEN nroot:= -1 * midpt; IF (X >= 0) THEN NROOT:= MIDPT; IF (X < 0) AND (N MOD 2 = 0) THEN HALT; end;{nroot} Continued in my posts below is some output from my program above.

[@ROCCOANDROXY]

+ROCCO DALTO Below is some output using the above program:c = 9 > rad(a * b * c))^6/5 = 8.585814487 where a = 1 b = 8 c = 9 > rad(a * b * c))^7/6 = 8.088036928 where a = 1 b = 8 c = 9 > rad(a * b * c))^8/7 = 7.750250053 where a = 1 b = 8 c = 9 > rad(a * b * c))^9/8 = 7.506200429 where a = 1 b = 8 c = 9 > rad(a * b * c))^10/9 = 7.321709615 where a = 1 b = 8 c = 9 > rad(a * b * c))^11/10 = 7.177387193 where a = 1 b = 8 c = 9 > rad(a * b * c))^12/11 = 7.061423738 where a = 1 b = 8 c = 9 > rad(a * b * c))^13/12 = 6.966220034 where a = 1 b = 8 c = 9 > rad(a * b * c))^14/13 = 6.886666293 where a = 1 b = 8 c = 9 > rad(a * b * c))^15/14 = 6.819200856 where a = 1 b = 8 c = 9 > rad(a * b * c))^16/15 = 6.761265661 where a = 1 b = 8 c = 9 > rad(a * b * c))^17/16 = 6.710976276 where a = 1 b = 8 c = 9 > rad(a * b * c))^18/17 = 6.666914006 where a = 1 b = 8 c = 9 > rad(a * b * c))^19/18 = 6.627990472 where a = 1 b = 8 c = 9 > rad(a * b * c))^20/19 = 6.593356817 where a = 1 b = 8 c = 9 > rad(a * b * c))^21/20 = 6.562341286 where a = 1 b = 8 c = 9 > rad(a * b * c))^22/21 = 6.534405353 where a = 1 b = 8 c = 9 > rad(a * b * c))^23/22 = 6.509112261 where a = 1 b = 8 c = 9 > rad(a * b * c))^24/23 = 6.486104081 where a = 1 b = 8 c = 9 > rad(a * b * c))^25/24 = 6.465084702 where a = 1 b = 8 c = 9 > rad(a * b * c))^26/25 = 6.445807039 where a = 1 b = 8 c = 9 > rad(a * b * c))^27/26 = 6.428063297 where a = 1 b = 8 c = 9 > rad(a * b * c))^28/27 = 6.411677461 where a = 1 b = 8 c = 9 > rad(a * b * c))^29/28 = 6.396499444 where a = 1 b = 8 c = 9 > rad(a * b * c))^30/29 = 6.382400487 where a = 1 b = 8 c = 9 > rad(a * b * c))^31/30 = 6.369269500 where a = 1 b = 8 c = 49 > rad(a * b * c))^26/25 = 48.772976685 where a = 1 b = 48 c = 49 > rad(a * b * c))^27/26 = 48.493324149 where a = 1 b = 48 c = 49 > rad(a * b * c))^28/27 = 48.235816517 where a = 1 b = 48 c = 49 > rad(a * b * c))^29/28 = 47.997926830 where a = 1 b = 48 c = 49 > rad(a * b * c))^30/29 = 47.777498096 where a = 1 b = 48 c = 49 > rad(a * b * c))^31/30 = 47.572678034 where a = 1 b = 48 c = 64 > rad(a * b * c))^10/9 = 63.622440269 where a = 1 b = 63 c = 64 > rad(a * b * c))^11/10 = 61.034335332 where a = 1 b = 63 c = 64 > rad(a * b * c))^12/11 = 58.995299156 where a = 1 b = 63 c = 64 > rad(a * b * c))^13/12 = 57.348236107 where a = 1 b = 63 c = 64 > rad(a * b * c))^14/13 = 55.990535406 where a = 1 b = 63 c = 64 > rad(a * b * c))^15/14 = 54.852404286 where a = 1 b = 63 c = 64 > rad(a * b * c))^16/15 = 53.884754651 where a = 1 b = 63 c = 64 > rad(a * b * c))^17/16 = 53.052074527 where a = 1 b = 63 c = 64 > rad(a * b * c))^18/17 = 52.328048997 where a = 1 b = 63 c = 64 > rad(a * b * c))^19/18 = 51.692770204 where a = 1 b = 63 c = 64 > rad(a * b * c))^20/19 = 51.130903106 where a = 1 b = 63 c = 64 > rad(a * b * c))^21/20 = 50.630446215 where a = 1 b = 63 c = 64 > rad(a * b * c))^22/21 = 50.181874001 where a = 1 b = 63 c = 64 > rad(a * b * c))^23/22 = 49.777530719 where a = 1 b = 63 c = 64 > rad(a * b * c))^24/23 = 49.411193767 where a = 1 b = 63 c = 64 > rad(a * b * c))^25/24 = 49.077753784 where a = 1 b = 63 c = 64 > rad(a * b * c))^26/25 = 48.772976685 where a = 1 b = 63 c = 64 > rad(a * b * c))^27/26 = 48.493324149 where a = 1 b = 63 c = 64 > rad(a * b * c))^28/27 = 48.235816517 where a = 1 b = 63 c = 64 > rad(a * b * c))^29/28 = 47.997926830 where a = 1 b = 63 c = 64 > rad(a * b * c))^30/29 = 47.777498096 where a = 1 b = 63 c = 64 > rad(a * b * c))^31/30 = 47.572678034 where a = 1 b = 63 c = 81 > rad(a * b * c))^5/4 = 70.210419580 where a = 1 b = 80 c = 81 > rad(a * b * c))^6/5 = 59.230514575 where a = 1 b = 80 c = 81 > rad(a * b * c))^7/6 = 52.882031498 where a = 1 b = 80 c = 81 > rad(a * b * c))^8/7 = 48.768407792 where a = 1 b = 80 c = 81 > rad(a * b * c))^9/8 = 45.894581242 where a = 1 b = 80 c = 81 > rad(a * b * c))^10/9 = 43.776984089 where a = 1 b = 80 c = 81 > rad(a * b * c))^11/10 = 42.153474795 where a = 1 b = 80 c = 81 > rad(a * b * c))^12/11 = 40.870034578 where a = 1 b = 80 c = 81 > rad(a * b * c))^13/12 = 39.830402269 where a = 1 b = 80 c = 81 > rad(a * b * c))^14/13 = 38.971396325 where a = 1 b = 80 c = 81 > rad(a * b * c))^15/14 = 38.249865801 where a = 1 b = 80 c = 81 > rad(a * b * c))^16/15 = 37.635353970 where a = 1 b = 80 c = 81 > rad(a * b * c))^17/16 = 37.105760163 where a = 1 b = 80 c = 81 > rad(a * b * c))^18/17 = 36.644663692 where a = 1 b = 80 c = 81 > rad(a * b * c))^19/18 = 36.239612617 where a = 1 b = 80 c = 81 > rad(a * b * c))^20/19 = 35.880995073 where a = 1 b = 80 c = 81 > rad(a * b * c))^21/20 = 35.561274497 where a = 1 b = 80 c = 81 > rad(a * b * c))^22/21 = 35.274459027 where a = 1 b = 80 c = 81 > rad(a * b * c))^23/22 = 35.015725572 where a = 1 b = 80 c = 81 > rad(a * b * c))^24/23 = 34.781148446 where a = 1 b = 80 c = 81 > rad(a * b * c))^25/24 = 34.567500171 where a = 1 b = 80 c = 81 > rad(a * b * c))^26/25 = 34.372103029 where a = 1 b = 80 c = 81 > rad(a * b * c))^27/26 = 34.192716911 where a = 1 b = 80 c = 81 > rad(a * b * c))^28/27 = 34.027453513 where a = 1 b = 80 c = 81 > rad(a * b * c))^29/28 = 33.874709947 where a = 1 b = 80 c = 81 > rad(a * b * c))^30/29 = 33.733116827 where a = 1 b = 80 c = 81 > rad(a * b * c))^31/30 = 33.601497274 where a = 1 b = 80 c = 243 > rad(a * b * c))^5/4 = 188.117812263 where a = 1 b = 242 c = 243 > rad(a * b * c))^6/5 = 152.564230416 where a = 1 b = 242 c = 243 > rad(a * b * c))^7/6 = 132.678715436 where a = 1 b = 242 c = 243 > rad(a * b * c))^8/7 = 120.082240798 where a = 1 b = 242 c = 243 > rad(a * b * c))^9/8 = 111.426099319 where a = 1 b = 242 c = 243 > rad(a * b * c))^10/9 = 105.127293568 where a = 1 b = 242 c = 243 > rad(a * b * c))^11/10 = 100.345598845 where a = 1 b = 242 c = 243 > rad(a * b * c))^12/11 = 96.595527971 where a = 1 b = 242 c = 243 > rad(a * b * c))^13/12 = 93.577749592 where a = 1 b = 242 c = 243 > rad(a * b * c))^14/13 = 91.098002359 where a = 1 b = 242 c = 243 > rad(a * b * c))^15/14 = 89.024872326 where a = 1 b = 242 c = 243 > rad(a * b * c))^16/15 = 87.266360654 where a = 1 b = 242 c = 243 > rad(a * b * c))^17/16 = 85.756180856 where a = 1 b = 242 c = 243 > rad(a * b * c))^18/17 = 84.445387274 where a = 1 b = 242 c = 243 > rad(a * b * c))^19/18 = 83.297067028 where a = 1 b = 242 c = 243 > rad(a * b * c))^20/19 = 82.282865168 where a = 1 b = 242 c = 243 > rad(a * b * c))^21/20 = 81.380645879 where a = 1 b = 242 c = 243 > rad(a * b * c))^22/21 = 80.572879535 where a = 1 b = 242 c = 243 > rad(a * b * c))^23/22 = 79.845506111 where a = 1 b = 242 c = 243 > rad(a * b * c))^24/23 = 79.187118774 where a = 1 b = 242 c = 243 > rad(a * b * c))^25/24 = 78.588367289 where a = 1 b = 242 c = 243 > rad(a * b * c))^26/25 = 78.041515236 where a = 1 b = 242 c = 243 > rad(a * b * c))^27/26 = 77.540106756 where a = 1 b = 242 c = 243 > rad(a * b * c))^28/27 = 77.078712492 where a = 1 b = 242 c = 243 > rad(a * b * c))^29/28 = 76.652733634 where a = 1 b = 242 c = 243 > rad(a * b * c))^30/29 = 76.258249149 where a = 1 b = 242 c = 243 > rad(a * b * c))^31/30 = 75.891895504 where a = 1 b = 242

[@ROCCOANDROXY]

+ROCCO DALTO c = 289 > rad(a * b * c))^6/5 = 257.229163909 where a = 1 b = 288 c = 289 > rad(a * b * c))^7/6 = 220.478815513 where a = 1 b = 288 c = 289 > rad(a * b * c))^8/7 = 197.489064894 where a = 1 b = 288 c = 289 > rad(a * b * c))^9/8 = 181.834042183 where a = 1 b = 288 c = 289 > rad(a * b * c))^10/9 = 170.521038390 where a = 1 b = 288 c = 289 > rad(a * b * c))^11/10 = 161.979550310 where a = 1 b = 288 c = 289 > rad(a * b * c))^12/11 = 155.310274532 where a = 1 b = 288 c = 289 > rad(a * b * c))^13/12 = 149.962792660 where a = 1 b = 288 c = 289 > rad(a * b * c))^14/13 = 145.582065661 where a = 1 b = 288 c = 289 > rad(a * b * c))^15/14 = 141.929153521 where a = 1 b = 288 c = 289 > rad(a * b * c))^16/15 = 138.837520781 where a = 1 b = 288 c = 289 > rad(a * b * c))^17/16 = 136.187636380 where a = 1 b = 288 c = 289 > rad(a * b * c))^18/17 = 133.891535765 where a = 1 b = 288 c = 289 > rad(a * b * c))^19/18 = 131.883076685 where a = 1 b = 288 c = 289 > rad(a * b * c))^20/19 = 130.111585858 where a = 1 b = 288 c = 289 > rad(a * b * c))^21/20 = 128.537598125 where a = 1 b = 288 c = 289 > rad(a * b * c))^22/21 = 127.129927403 where a = 1 b = 288 c = 289 > rad(a * b * c))^23/22 = 125.863608729 where a = 1 b = 288 c = 289 > rad(a * b * c))^24/23 = 124.718423927 where a = 1 b = 288 c = 289 > rad(a * b * c))^25/24 = 123.677826838 where a = 1 b = 288 c = 289 > rad(a * b * c))^26/25 = 122.728147430 where a = 1 b = 288 c = 289 > rad(a * b * c))^27/26 = 121.857993982 where a = 1 b = 288 c = 289 > rad(a * b * c))^28/27 = 121.057798205 where a = 1 b = 288 c = 289 > rad(a * b * c))^29/28 = 120.319465005 where a = 1 b = 288 c = 289 > rad(a * b * c))^30/29 = 119.636099880 where a = 1 b = 288 c = 289 > rad(a * b * c))^31/30 = 119.001794607 where a = 1 b = 288 c = 513 > rad(a * b * c))^5/4 = 372.504105968 where a = 1 b = 512 c = 513 > rad(a * b * c))^6/5 = 293.958363945 where a = 1 b = 512 c = 513 > rad(a * b * c))^7/6 = 251.028092821 where a = 1 b = 512 c = 513 > rad(a * b * c))^8/7 = 224.258235911 where a = 1 b = 512 c = 513 > rad(a * b * c))^9/8 = 206.071512054 where a = 1 b = 512 c = 513 > rad(a * b * c))^10/9 = 192.952244495 where a = 1 b = 512 c = 513 > rad(a * b * c))^11/10 = 183.060791787 where a = 1 b = 512 c = 513 > rad(a * b * c))^12/11 = 175.346136577 where a = 1 b = 512 c = 513 > rad(a * b * c))^13/12 = 169.166198106 where a = 1 b = 512 c = 513 > rad(a * b * c))^14/13 = 164.107451600 where a = 1 b = 512 c = 513 > rad(a * b * c))^15/14 = 159.891960066 where a = 1 b = 512 c = 513 > rad(a * b * c))^16/15 = 156.326225306 where a = 1 b = 512 c = 513 > rad(a * b * c))^17/16 = 153.271498897 where a = 1 b = 512 c = 513 > rad(a * b * c))^18/17 = 150.625761092 where a = 1 b = 512 c = 513 > rad(a * b * c))^19/18 = 148.312359136 where a = 1 b = 512 c = 513 > rad(a * b * c))^20/19 = 146.272606853 where a = 1 b = 512 c = 513 > rad(a * b * c))^21/20 = 144.460826052 where a = 1 b = 512 c = 513 > rad(a * b * c))^22/21 = 142.840940621 where a = 1 b = 512 c = 513 > rad(a * b * c))^23/22 = 141.384085277 where a = 1 b = 512 c = 513 > rad(a * b * c))^24/23 = 140.066893620 where a = 1 b = 512 c = 513 > rad(a * b * c))^25/24 = 138.870250897 where a = 1 b = 512 c = 513 > rad(a * b * c))^26/25 = 137.778370922 where a = 1 b = 512 c = 513 > rad(a * b * c))^27/26 = 136.778103081 where a = 1 b = 512 c = 513 > rad(a * b * c))^28/27 = 135.858405282 where a = 1 b = 512 c = 513 > rad(a * b * c))^29/28 = 135.009938329 where a = 1 b = 512 c = 513 > rad(a * b * c))^30/29 = 134.224750337 where a = 1 b = 512 c = 513 > rad(a * b * c))^31/30 = 133.496028723 where a = 1 b = 512 c = 625 > rad(a * b * c))^14/13 = 617.130867092 where a = 1 b = 624 c = 625 > rad(a * b * c))^15/14 = 597.228673435 where a = 1 b = 624 c = 625 > rad(a * b * c))^16/15 = 580.500031305 where a = 1 b = 624 c = 625 > rad(a * b * c))^17/16 = 566.247300988 where a = 1 b = 624 c = 625 > rad(a * b * c))^18/17 = 553.962252037 where a = 1 b = 624 c = 625 > rad(a * b * c))^19/18 = 543.266143786 where a = 1 b = 624 c = 625 > rad(a * b * c))^20/19 = 533.871120384 where a = 1 b = 624 c = 625 > rad(a * b * c))^21/20 = 525.554594804 where a = 1 b = 624 c = 625 > rad(a * b * c))^22/21 = 518.141807681 where a = 1 b = 624 c = 625 > rad(a * b * c))^23/22 = 511.493678858 where a = 1 b = 624 c = 625 > rad(a * b * c))^24/23 = 505.498172607 where a = 1 b = 624 c = 625 > rad(a * b * c))^25/24 = 500.064048184 where a = 1 b = 624 c = 625 > rad(a * b * c))^26/25 = 495.116262481 where a = 1 b = 624 c = 625 > rad(a * b * c))^27/26 = 490.592537821 where a = 1 b = 624 c = 625 > rad(a * b * c))^28/27 = 486.440765052 where a = 1 b = 624 c = 625 > rad(a * b * c))^29/28 = 482.617014453 where a = 1 b = 624 c = 625 > rad(a * b * c))^30/29 = 479.083995039 where a = 1 b = 624 c = 625 > rad(a * b * c))^31/30 = 475.809848793 where a = 1 b = 624 c = 676 > rad(a * b * c))^12/11 = 670.835342337 where a = 1 b = 675 c = 676 > rad(a * b * c))^13/12 = 641.189877658 where a = 1 b = 675 c = 676 > rad(a * b * c))^14/13 = 617.130867092 where a = 1 b = 675 c = 676 > rad(a * b * c))^15/14 = 597.228673435 where a = 1 b = 675 c = 676 > rad(a * b * c))^16/15 = 580.500031305 where a = 1 b = 675 c = 676 > rad(a * b * c))^17/16 = 566.247300988 where a = 1 b = 675 c = 676 > rad(a * b * c))^18/17 = 553.962252037 where a = 1 b = 675 c = 676 > rad(a * b * c))^19/18 = 543.266143786 where a = 1 b = 675 c = 676 > rad(a * b * c))^20/19 = 533.871120384 where a = 1 b = 675 c = 676 > rad(a * b * c))^21/20 = 525.554594804 where a = 1 b = 675 c = 676 > rad(a * b * c))^22/21 = 518.141807681 where a = 1 b = 675 c = 676 > rad(a * b * c))^23/22 = 511.493678858 where a = 1 b = 675 c = 676 > rad(a * b * c))^24/23 = 505.498172607 where a = 1 b = 675 c = 676 > rad(a * b * c))^25/24 = 500.064048184 where a = 1 b = 675 c = 676 > rad(a * b * c))^26/25 = 495.116262481 where a = 1 b = 675 c = 676 > rad(a * b * c))^27/26 = 490.592537821 where a = 1 b = 675 c = 676 > rad(a * b * c))^28/27 = 486.440765052 where a = 1 b = 675 c = 676 > rad(a * b * c))^29/28 = 482.617014453 where a = 1 b = 675 c = 676 > rad(a * b * c))^30/29 = 479.083995039 where a = 1 b = 675 c = 676 > rad(a * b * c))^31/30 = 475.809848793 where a = 1 b = 675

[@ROCCOANDROXY]

+ROCCO DALTO c = 3025 > rad(a * b * c))^30/29 = 3017.161795630 where a = 1 b = 3024 c = 3025 > rad(a * b * c))^31/30 = 2990.421312453 where a = 1 b = 3024 c = 3888 > rad(a * b * c))^11/10 = 3794.937979015 where a = 1 b = 3887 c = 3888 > rad(a * b * c))^12/11 = 3545.067253412 where a = 1 b = 3887 c = 3888 > rad(a * b * c))^13/12 = 3349.456243161 where a = 1 b = 3887 c = 3888 > rad(a * b * c))^14/13 = 3192.393901205 where a = 1 b = 3887 c = 3888 > rad(a * b * c))^15/14 = 3063.644204300 where a = 1 b = 3887 c = 3888 > rad(a * b * c))^16/15 = 2956.268900016 where a = 1 b = 3887 c = 3888 > rad(a * b * c))^17/16 = 2865.407155839 where a = 1 b = 3887 c = 3888 > rad(a * b * c))^18/17 = 2787.557013005 where a = 1 b = 3887 c = 3888 > rad(a * b * c))^19/18 = 2720.134332411 where a = 1 b = 3887 c = 3888 > rad(a * b * c))^20/19 = 2661.192257724 where a = 1 b = 3887 c = 3888 > rad(a * b * c))^21/20 = 2609.237193962 where a = 1 b = 3887 c = 3888 > rad(a * b * c))^22/21 = 2563.104802476 where a = 1 b = 3887 c = 3888 > rad(a * b * c))^23/22 = 2521.874432366 where a = 1 b = 3887 c = 3888 > rad(a * b * c))^24/23 = 2484.808817574 where a = 1 b = 3887 c = 3888 > rad(a * b * c))^25/24 = 2451.310771859 where a = 1 b = 3887 c = 3888 > rad(a * b * c))^26/25 = 2420.891559509 where a = 1 b = 3887 c = 3888 > rad(a * b * c))^27/26 = 2393.147437740 where a = 1 b = 3887 c = 3888 > rad(a * b * c))^28/27 = 2367.742016176 where a = 1 b = 3887 c = 3888 > rad(a * b * c))^29/28 = 2344.392821716 where a = 1 b = 3887 c = 3888 > rad(a * b * c))^30/29 = 2322.860946836 where a = 1 b = 3887 c = 3888 > rad(a * b * c))^31/30 = 2302.942988141 where a = 1 b = 3887 c = 3969 > rad(a * b * c))^8/7 = 3627.065601193 where a = 1 b = 3968 c = 3969 > rad(a * b * c))^9/8 = 3191.077540124 where a = 1 b = 3968 c = 3969 > rad(a * b * c))^10/9 = 2888.543228553 where a = 1 b = 3968 c = 3969 > rad(a * b * c))^11/10 = 2667.301336985 where a = 1 b = 3968 c = 3969 > rad(a * b * c))^12/11 = 2498.949255830 where a = 1 b = 3968 c = 3969 > rad(a * b * c))^13/12 = 2366.801847359 where a = 1 b = 3968 c = 3969 > rad(a * b * c))^14/13 = 2260.458012682 where a = 1 b = 3968 c = 3969 > rad(a * b * c))^15/14 = 2173.117441086 where a = 1 b = 3968 c = 3969 > rad(a * b * c))^16/15 = 2100.156779059 where a = 1 b = 3968 c = 3969 > rad(a * b * c))^17/16 = 2038.328471381 where a = 1 b = 3968 c = 3969 > rad(a * b * c))^18/17 = 1985.287440259 where a = 1 b = 3968 c = 3969 > rad(a * b * c))^19/18 = 1939.299688954 where a = 1 b = 3968 c = 3969 > rad(a * b * c))^20/19 = 1899.056466099 where a = 1 b = 3968 c = 3969 > rad(a * b * c))^21/20 = 1863.552076212 where a = 1 b = 3968 c = 3969 > rad(a * b * c))^22/21 = 1832.001365363 where a = 1 b = 3968 c = 3969 > rad(a * b * c))^23/22 = 1803.782672910 where a = 1 b = 3968 c = 3969 > rad(a * b * c))^24/23 = 1778.397557060 where a = 1 b = 3968 c = 3969 > rad(a * b * c))^25/24 = 1755.441826226 where a = 1 b = 3968 c = 3969 > rad(a * b * c))^26/25 = 1734.584349519 where a = 1 b = 3968 c = 3969 > rad(a * b * c))^27/26 = 1715.551320279 where a = 1 b = 3968 c = 3969 > rad(a * b * c))^28/27 = 1698.114407044 where a = 1 b = 3968 c = 3969 > rad(a * b * c))^29/28 = 1682.081718673 where a = 1 b = 3968 c = 3969 > rad(a * b * c))^30/29 = 1667.290835431 where a = 1 b = 3968 c = 3969 > rad(a * b * c))^31/30 = 1653.603376368 where a = 1 b = 3968 c = 4096 > rad(a * b * c))^21/20 = 4054.812525620 where a = 1 b = 4095 c = 4096 > rad(a * b * c))^22/21 = 3979.142018913 where a = 1 b = 4095 c = 4096 > rad(a * b * c))^23/22 = 3911.576769873 where a = 1 b = 4095 c = 4096 > rad(a * b * c))^24/23 = 3850.889199710 where a = 1 b = 4095 c = 4096 > rad(a * b * c))^25/24 = 3796.086418657 where a = 1 b = 4095 c = 4096 > rad(a * b * c))^26/25 = 3746.356938515 where a = 1 b = 4095 c = 4096 > rad(a * b * c))^27/26 = 3701.031222165 where a = 1 b = 4095 c = 4096 > rad(a * b * c))^28/27 = 3659.552064605 where a = 1 b = 4095 c = 4096 > rad(a * b * c))^29/28 = 3621.452069170 where a = 1 b = 4095 c = 4096 > rad(a * b * c))^30/29 = 3586.336317599 where a = 1 b = 4095 c = 4096 > rad(a * b * c))^31/30 = 3553.868892054 where a = 1 b = 4095 c = 4375 > rad(a * b * c))^3/2 = 3043.189116701 where a = 1 b = 4374 c = 4375 > rad(a * b * c))^4/3 = 1248.223610081 where a = 1 b = 4374 c = 4375 > rad(a * b * c))^5/4 = 799.418360126 where a = 1 b = 4374 c = 4375 > rad(a * b * c))^6/5 = 611.875626301 where a = 1 b = 4374 c = 4375 > rad(a * b * c))^7/6 = 511.983357266 where a = 1 b = 4374 c = 4375 > rad(a * b * c))^8/7 = 450.780279257 where a = 1 b = 4374 c = 4375 > rad(a * b * c))^9/8 = 409.729002667 where a = 1 b = 4374 c = 4375 > rad(a * b * c))^10/9 = 380.402761339 where a = 1 b = 4374 c = 4375 > rad(a * b * c))^11/10 = 358.460432298 where a = 1 b = 4374 c = 4375 > rad(a * b * c))^12/11 = 341.452376473 where a = 1 b = 4374 c = 4375 > rad(a * b * c))^13/12 = 327.897095177 where a = 1 b = 4374 c = 4375 > rad(a * b * c))^14/13 = 316.848421726 where a = 1 b = 4374 c = 4375 > rad(a * b * c))^15/14 = 307.674923651 where a = 1 b = 4374 c = 4375 > rad(a * b * c))^16/15 = 299.939673499 where a = 1 b = 4374 c = 4375 > rad(a * b * c))^17/16 = 293.331025567 where a = 1 b = 4374 c = 4375 > rad(a * b * c))^18/17 = 287.620892590 where a = 1 b = 4374 c = 4375 > rad(a * b * c))^19/18 = 282.638602957 where a = 1 b = 4374 c = 4375 > rad(a * b * c))^20/19 = 278.253965843 where a = 1 b = 4374 c = 4375 > rad(a * b * c))^21/20 = 274.365979638 where a = 1 b = 4374 c = 4375 > rad(a * b * c))^22/21 = 270.895110233 where a = 1 b = 4374 c = 4375 > rad(a * b * c))^23/22 = 267.777891282 where a = 1 b = 4374 c = 4375 > rad(a * b * c))^24/23 = 264.963072398 where a = 1 b = 4374 c = 4375 > rad(a * b * c))^25/24 = 262.408822236 where a = 1 b = 4374 c = 4375 > rad(a * b * c))^26/25 = 260.080664752 where a = 1 b = 4374 c = 4375 > rad(a * b * c))^27/26 = 257.949934217 where a = 1 b = 4374 c = 4375 > rad(a * b * c))^28/27 = 255.992603216 where a = 1 b = 4374 c = 4375 > rad(a * b * c))^29/28 = 254.188382832 where a = 1 b = 4374 c = 4375 > rad(a * b * c))^30/29 = 252.520024120 where a = 1 b = 4374 c = 4375 > rad(a * b * c))^31/30 = 250.972770305 where a = 1 b = 4374 c = 128 > rad(a * b * c))^4/3 = 93.216975179 where a = 3 b = 125 c = 128 > rad(a * b * c))^5/4 = 70.210419580 where a = 3 b = 125 c = 128 > rad(a * b * c))^6/5 = 59.230514575 where a = 3 b = 125 c = 128 > rad(a * b * c))^7/6 = 52.882031498 where a = 3 b = 125 c = 128 > rad(a * b * c))^8/7 = 48.768407792 where a = 3 b = 125 c = 128 > rad(a * b * c))^9/8 = 45.894581242 where a = 3 b = 125 c = 128 > rad(a * b * c))^10/9 = 43.776984089 where a = 3 b = 125 c = 128 > rad(a * b * c))^11/10 = 42.153474795 where a = 3 b = 125 c = 128 > rad(a * b * c))^12/11 = 40.870034578 where a = 3 b = 125 c = 128 > rad(a * b * c))^13/12 = 39.830402269 where a = 3 b = 125 c = 128 > rad(a * b * c))^14/13 = 38.971396325 where a = 3 b = 125 c = 128 > rad(a * b * c))^15/14 = 38.249865801 where a = 3 b = 125 c = 128 > rad(a * b * c))^16/15 = 37.635353970 where a = 3 b = 125 c = 128 > rad(a * b * c))^17/16 = 37.105760163 where a = 3 b = 125 c = 128 > rad(a * b * c))^18/17 = 36.644663692 where a = 3 b = 125 c = 128 > rad(a * b * c))^19/18 = 36.239612617 where a = 3 b = 125 c = 128 > rad(a * b * c))^20/19 = 35.880995073 where a = 3 b = 125 c = 128 > rad(a * b * c))^21/20 = 35.561274497 where a = 3 b = 125 c = 128 > rad(a * b * c))^22/21 = 35.274459027 where a = 3 b = 125 c = 128 > rad(a * b * c))^23/22 = 35.015725572 where a = 3 b = 125 c = 128 > rad(a * b * c))^24/23 = 34.781148446 where a = 3 b = 125 c = 128 > rad(a * b * c))^25/24 = 34.567500171 where a = 3 b = 125 c = 128 > rad(a * b * c))^26/25 = 34.372103029 where a = 3 b = 125 c = 128 > rad(a * b * c))^27/26 = 34.192716911 where a = 3 b = 125 c = 128 > rad(a * b * c))^28/27 = 34.027453513 where a = 3 b = 125 c = 128 > rad(a * b * c))^29/28 = 33.874709947 where a = 3 b = 125 c = 128 > rad(a * b * c))^30/29 = 33.733116827 where a = 3 b = 125 c = 128 > rad(a * b * c))^31/30 = 33.601497274 where a = 3 b = 125

[@ROCCOANDROXY]

+ROCCO DALTO c = 512 > rad(a * b * c))^23/22 = 511.493678858 where a = 5 b = 507 c = 512 > rad(a * b * c))^24/23 = 505.498172607 where a = 5 b = 507 c = 512 > rad(a * b * c))^25/24 = 500.064048184 where a = 5 b = 507 c = 512 > rad(a * b * c))^26/25 = 495.116262481 where a = 5 b = 507 c = 512 > rad(a * b * c))^27/26 = 490.592537821 where a = 5 b = 507 c = 512 > rad(a * b * c))^28/27 = 486.440765052 where a = 5 b = 507 c = 512 > rad(a * b * c))^29/28 = 482.617014453 where a = 5 b = 507 c = 512 > rad(a * b * c))^30/29 = 479.083995039 where a = 5 b = 507 c = 512 > rad(a * b * c))^31/30 = 475.809848793 where a = 5 b = 507 c = 1029 > rad(a * b * c))^5/4 = 799.418360126 where a = 5 b = 1024 c = 1029 > rad(a * b * c))^6/5 = 611.875626301 where a = 5 b = 1024 c = 1029 > rad(a * b * c))^7/6 = 511.983357266 where a = 5 b = 1024 c = 1029 > rad(a * b * c))^8/7 = 450.780279257 where a = 5 b = 1024 c = 1029 > rad(a * b * c))^9/8 = 409.729002667 where a = 5 b = 1024 c = 1029 > rad(a * b * c))^10/9 = 380.402761339 where a = 5 b = 1024 c = 1029 > rad(a * b * c))^11/10 = 358.460432298 where a = 5 b = 1024 c = 1029 > rad(a * b * c))^12/11 = 341.452376473 where a = 5 b = 1024 c = 1029 > rad(a * b * c))^13/12 = 327.897095177 where a = 5 b = 1024 c = 1029 > rad(a * b * c))^14/13 = 316.848421726 where a = 5 b = 1024 c = 1029 > rad(a * b * c))^15/14 = 307.674923651 where a = 5 b = 1024 c = 1029 > rad(a * b * c))^16/15 = 299.939673499 where a = 5 b = 1024 c = 1029 > rad(a * b * c))^17/16 = 293.331025567 where a = 5 b = 1024 c = 1029 > rad(a * b * c))^18/17 = 287.620892590 where a = 5 b = 1024 c = 1029 > rad(a * b * c))^19/18 = 282.638602957 where a = 5 b = 1024 c = 1029 > rad(a * b * c))^20/19 = 278.253965843 where a = 5 b = 1024 c = 1029 > rad(a * b * c))^21/20 = 274.365979638 where a = 5 b = 1024 c = 1029 > rad(a * b * c))^22/21 = 270.895110233 where a = 5 b = 1024 c = 1029 > rad(a * b * c))^23/22 = 267.777891282 where a = 5 b = 1024 c = 1029 > rad(a * b * c))^24/23 = 264.963072398 where a = 5 b = 1024 c = 1029 > rad(a * b * c))^25/24 = 262.408822236 where a = 5 b = 1024 c = 1029 > rad(a * b * c))^26/25 = 260.080664752 where a = 5 b = 1024 c = 1029 > rad(a * b * c))^27/26 = 257.949934217 where a = 5 b = 1024 c = 1029 > rad(a * b * c))^28/27 = 255.992603216 where a = 5 b = 1024 c = 1029 > rad(a * b * c))^29/28 = 254.188382832 where a = 5 b = 1024 c = 1029 > rad(a * b * c))^30/29 = 252.520024120 where a = 5 b = 1024 c = 1029 > rad(a * b * c))^31/30 = 250.972770305 where a = 5 b = 1024 c = 4000 > rad(a * b * c))^16/15 = 3871.263907347 where a = 7 b = 3993 c = 4000 > rad(a * b * c))^17/16 = 3748.329221452 where a = 7 b = 3993 c = 4000 > rad(a * b * c))^18/17 = 3643.103487129 where a = 7 b = 3993 c = 4000 > rad(a * b * c))^19/18 = 3552.051976556 where a = 7 b = 3993 c = 4000 > rad(a * b * c))^20/19 = 3472.515471370 where a = 7 b = 3993 c = 4000 > rad(a * b * c))^21/20 = 3402.456479466 where a = 7 b = 3993 c = 4000 > rad(a * b * c))^22/21 = 3340.288504476 where a = 7 b = 3993 c = 4000 > rad(a * b * c))^23/22 = 3284.758412163 where a = 7 b = 3993 c = 4000 > rad(a * b * c))^24/23 = 3234.863644090 where a = 7 b = 3993 c = 4000 > rad(a * b * c))^25/24 = 3189.792841375 where a = 7 b = 3993 c = 4000 > rad(a * b * c))^26/25 = 3148.882527346 where a = 7 b = 3993 c = 4000 > rad(a * b * c))^27/26 = 3111.585015801 where a = 7 b = 3993 c = 4000 > rad(a * b * c))^28/27 = 3077.444301272 where a = 7 b = 3993 c = 4000 > rad(a * b * c))^29/28 = 3046.077713722 where a = 7 b = 3993 c = 4000 > rad(a * b * c))^30/29 = 3017.161795630 where a = 7 b = 3993 c = 4000 > rad(a * b * c))^31/30 = 2990.421312453 where a = 7 b = 3993 c = 1331 > rad(a * b * c))^7/6 = 1284.543960254 where a = 8 b = 1323 c = 1331 > rad(a * b * c))^8/7 = 1109.954343231 where a = 8 b = 1323 c = 1331 > rad(a * b * c))^9/8 = 994.768953311 where a = 8 b = 1323 c = 1331 > rad(a * b * c))^10/9 = 913.510000693 where a = 8 b = 1323 c = 1331 > rad(a * b * c))^11/10 = 853.308699137 where a = 8 b = 1323 c = 1331 > rad(a * b * c))^12/11 = 807.016018523 where a = 8 b = 1323 c = 1331 > rad(a * b * c))^13/12 = 770.363102464 where a = 8 b = 1323 c = 1331 > rad(a * b * c))^14/13 = 740.652401293 where a = 8 b = 1323 c = 1331 > rad(a * b * c))^15/14 = 716.099788139 where a = 8 b = 1323 c = 1331 > rad(a * b * c))^16/15 = 695.480205742 where a = 8 b = 1323 c = 1331 > rad(a * b * c))^17/16 = 677.925701261 where a = 8 b = 1323 c = 1331 > rad(a * b * c))^18/17 = 662.804763798 where a = 8 b = 1323 c = 1331 > rad(a * b * c))^19/18 = 649.647304559 where a = 8 b = 1323 c = 1331 > rad(a * b * c))^20/19 = 638.096393570 where a = 8 b = 1323 c = 1331 > rad(a * b * c))^21/20 = 627.876276826 where a = 8 b = 1323 c = 1331 > rad(a * b * c))^22/21 = 618.770625705 where a = 8 b = 1323 c = 1331 > rad(a * b * c))^23/22 = 610.607402967 where a = 8 b = 1323 c = 1331 > rad(a * b * c))^24/23 = 603.248116351 where a = 8 b = 1323 c = 1331 > rad(a * b * c))^25/24 = 596.580047720 where a = 8 b = 1323 c = 1331 > rad(a * b * c))^26/25 = 590.510541161 where a = 8 b = 1323 c = 1331 > rad(a * b * c))^27/26 = 584.962741888 where a = 8 b = 1323 c = 1331 > rad(a * b * c))^28/27 = 579.872374404 where a = 8 b = 1323 c = 1331 > rad(a * b * c))^29/28 = 575.185276342 where a = 8 b = 1323 c = 1331 > rad(a * b * c))^30/29 = 570.855489377 where a = 8 b = 1323 c = 1331 > rad(a * b * c))^31/30 = 566.843766000 where a = 8 b = 1323 c = 2057 > rad(a * b * c))^13/12 = 2014.461299056 where a = 9 b = 2048 c = 2057 > rad(a * b * c))^14/13 = 1925.784522952 where a = 9 b = 2048 c = 2057 > rad(a * b * c))^15/14 = 1852.889369044 where a = 9 b = 2048 c = 2057 > rad(a * b * c))^16/15 = 1791.949284047 where a = 9 b = 2048 c = 2057 > rad(a * b * c))^17/16 = 1740.273113134 where a = 9 b = 2048 c = 2057 > rad(a * b * c))^18/17 = 1695.915468629 where a = 9 b = 2048 c = 2057 > rad(a * b * c))^19/18 = 1657.436522510 where a = 9 b = 2048 c = 2057 > rad(a * b * c))^20/19 = 1623.748626645 where a = 9 b = 2048 c = 2057 > rad(a * b * c))^21/20 = 1594.015351946 where a = 9 b = 2048 c = 2057 > rad(a * b * c))^22/21 = 1567.583241773 where a = 9 b = 2048 c = 2057 > rad(a * b * c))^23/22 = 1543.934585407 where a = 9 b = 2048 c = 2057 > rad(a * b * c))^24/23 = 1522.654050077 where a = 9 b = 2048 c = 2057 > rad(a * b * c))^25/24 = 1503.404661939 where a = 9 b = 2048 c = 2057 > rad(a * b * c))^26/25 = 1485.910224905 where a = 9 b = 2048 c = 2057 > rad(a * b * c))^27/26 = 1469.942255584 where a = 9 b = 2048 c = 2057 > rad(a * b * c))^28/27 = 1455.310139945 where a = 9 b = 2048 c = 2057 > rad(a * b * c))^29/28 = 1441.853623662 where a = 9 b = 2048 c = 2057 > rad(a * b * c))^30/29 = 1429.437016699 where a = 9 b = 2048 c = 2057 > rad(a * b * c))^31/30 = 1417.944673357 where a = 9 b = 2048

[@ROCCOANDROXY]

+ROCCO DALTO c = 2197 > rad(a * b * c))^5/4 = 1733.128479312 where a = 10 b = 2187 c = 2197 > rad(a * b * c))^6/5 = 1286.108262803 where a = 10 b = 2187 c = 2197 > rad(a * b * c))^7/6 = 1054.165280027 where a = 10 b = 2187 c = 2197 > rad(a * b * c))^8/7 = 914.569457367 where a = 10 b = 2187 c = 2197 > rad(a * b * c))^9/8 = 822.143604811 where a = 10 b = 2187 c = 2197 > rad(a * b * c))^10/9 = 756.764366625 where a = 10 b = 2187 c = 2197 > rad(a * b * c))^11/10 = 708.224697743 where a = 10 b = 2187 c = 2197 > rad(a * b * c))^12/11 = 670.835342337 where a = 10 b = 2187 c = 2197 > rad(a * b * c))^13/12 = 641.189877658 where a = 10 b = 2187 c = 2197 > rad(a * b * c))^14/13 = 617.130867092 where a = 10 b = 2187 c = 2197 > rad(a * b * c))^15/14 = 597.228673435 where a = 10 b = 2187 c = 2197 > rad(a * b * c))^16/15 = 580.500031305 where a = 10 b = 2187 c = 2197 > rad(a * b * c))^17/16 = 566.247300988 where a = 10 b = 2187 c = 2197 > rad(a * b * c))^18/17 = 553.962252037 where a = 10 b = 2187 c = 2197 > rad(a * b * c))^19/18 = 543.266143786 where a = 10 b = 2187 c = 2197 > rad(a * b * c))^20/19 = 533.871120384 where a = 10 b = 2187 c = 2197 > rad(a * b * c))^21/20 = 525.554594804 where a = 10 b = 2187 c = 2197 > rad(a * b * c))^22/21 = 518.141807681 where a = 10 b = 2187 c = 2197 > rad(a * b * c))^23/22 = 511.493678858 where a = 10 b = 2187 c = 2197 > rad(a * b * c))^24/23 = 505.498172607 where a = 10 b = 2187 c = 2197 > rad(a * b * c))^25/24 = 500.064048184 where a = 10 b = 2187 c = 2197 > rad(a * b * c))^26/25 = 495.116262481 where a = 10 b = 2187 c = 2197 > rad(a * b * c))^27/26 = 490.592537821 where a = 10 b = 2187 c = 2197 > rad(a * b * c))^28/27 = 486.440765052 where a = 10 b = 2187 c = 2197 > rad(a * b * c))^29/28 = 482.617014453 where a = 10 b = 2187 c = 2197 > rad(a * b * c))^30/29 = 479.083995039 where a = 10 b = 2187 c = 2197 > rad(a * b * c))^31/30 = 475.809848793 where a = 10 b = 2187 c = 2187 > rad(a * b * c))^12/11 = 2124.540110531 where a = 11 b = 2176 c = 2187 > rad(a * b * c))^13/12 = 2014.461299056 where a = 11 b = 2176 c = 2187 > rad(a * b * c))^14/13 = 1925.784522952 where a = 11 b = 2176 c = 2187 > rad(a * b * c))^15/14 = 1852.889369044 where a = 11 b = 2176 c = 2187 > rad(a * b * c))^16/15 = 1791.949284047 where a = 11 b = 2176 c = 2187 > rad(a * b * c))^17/16 = 1740.273113134 where a = 11 b = 2176 c = 2187 > rad(a * b * c))^18/17 = 1695.915468629 where a = 11 b = 2176 c = 2187 > rad(a * b * c))^19/18 = 1657.436522510 where a = 11 b = 2176 c = 2187 > rad(a * b * c))^20/19 = 1623.748626645 where a = 11 b = 2176 c = 2187 > rad(a * b * c))^21/20 = 1594.015351946 where a = 11 b = 2176 c = 2187 > rad(a * b * c))^22/21 = 1567.583241773 where a = 11 b = 2176 c = 2187 > rad(a * b * c))^23/22 = 1543.934585407 where a = 11 b = 2176 c = 2187 > rad(a * b * c))^24/23 = 1522.654050077 where a = 11 b = 2176 c = 2187 > rad(a * b * c))^25/24 = 1503.404661939 where a = 11 b = 2176 c = 2187 > rad(a * b * c))^26/25 = 1485.910224905 where a = 11 b = 2176 c = 2187 > rad(a * b * c))^27/26 = 1469.942255584 where a = 11 b = 2176 c = 2187 > rad(a * b * c))^28/27 = 1455.310139945 where a = 11 b = 2176 c = 2187 > rad(a * b * c))^29/28 = 1441.853623662 where a = 11 b = 2176 c = 2187 > rad(a * b * c))^30/29 = 1429.437016699 where a = 11 b = 2176 c = 2187 > rad(a * b * c))^31/30 = 1417.944673357 where a = 11 b = 2176

[@AdamFerrari64]

For those watching in 2023: This proof has STILL not been accepted by the community. So the A B C conjecture is still unsolved 😮

[@peterlindner3283]

What I like is that the wikipedia entry I can't understand, yet I can understand this EXCELLENT video.

[@Edlandish]

Digging the pigeon wallpaper. And also that bit about the radical being well wicked.

[@BenWard29]

Sooo…. how’s the check process going on this. 10 years should be enough time, right? It’s ONLY 500 pages and Mochizuki is notoriously difficult to deal with. I know that Peter Scholze was working with him, but that didn’t pan out. Would be curious for a follow-up (if you haven’t already done it).

[@ijeremyoliver]

I like the way this guy nerds out about numbers. He gets excited, and that has precedence over getting US to be excited about it. He's happy just being happy. He does, of course, explain some of these things. Otherwise, these videos would be very short. But, he explains them so we can understand them. He's not forcing US to be passionate about them. It's great. I really admire that.

[@moyosoofficial5042]

Props to that Japanese guy for writing all these papers in his second language. Including one that's part of a 4 part series and the first part is over 130 pages long, all in English

[@Henry14arsenal2007]

So after 6 years maybe you should do another video about the progress that has been made at understanding the proof.

[@burthpinmc5489]

Henry14arsenal2007 What, you expect some beyond Ph.D level algebraic geometry and number field theory papers to be explained easy just for people on youtube? Impossible

[@Henry14arsenal2007]

Wishful thinking on my part.

[@jacks.4390]

Ever since this video came out, I've been googling the latest news every few months. The proof is still not fully verified; however, the consensus seems to be that it's probably not correct. Many people who have studied it have said that when you start reading it, there is a lot of stuff that's easy to understand, but then you just come across some insurmountable roadblocks; the author claims some things that he doesn't prove, and the people reading it do not see a way it can be proved. For a long time the author was not very helpul; he wouldn't want to leave Japan to give talks, and when he was asked questions he would just say stuff like "read it more and you will understand". However, I think I read a few months ago on a blog that recently some of the top mathematicians in that field have found a concrete error and are getting ready to present it.

[@gJonii]

It's probably bunk anyway.

[@cube2fox]

@@burthpinmc5489 It's probably not just "beyond Ph.D level" but "beyond world's best experts in the field level".

[@jamiedodds3562]

2019 and Mochizuki's proof's still being examined

[@gytoser801]

2022 and is still being examined

[@epicm999]

2023 and still being examined.

[@yugi123445]

I really like these guys videos! They are just happy about what they are doing, the topics are so interesting; this is what really makes difference and how math should always be taught, whether it is abstract or fact. Thank you for that, though didn't really have to try that hard presume.

[@frankdrebiin]

that is the really cool stuff of mathematics.. please do more of these.. i like theorems and proovs etc

[@champion171299]

4:05 "It's called radical, cos it's well wicked" xD made me laugh so much!

[@numberphile]

Protection was in place!

[@delve_]

_Me, assuring my partner who doesn't want us to get pregnant_

[@isaacanwarwatts8844]

What

[@unvergebeneid]

Wow, this was over three years ago and we still don't know if the proof is correct. Can I just say that this means that Shinichi Mochizuki is a frickin' genius no matter what?

[@maverickvigor9582]

+Penny Lane Definitely, and 3 years is just 3 years when it comes to such a densed "script" we got there to follow and work on it but the sad part of this is that it's not being studied or analyzed much or at least paying much attention to it, which we could slowly and naturally help about it each of us little by little. But yes, he definitely must be a genius and by my book he is.

[@maverickvigor9582]

***** I'm not selling, it's an exclusive original, you gotta earn it. it's on you and for you, you take it or you leave it.

[@NathanTAK]

I can write a 500 page document of dense notation that means nothing. In other words: I have a marvelously undecipherable maybe-proof of an obscure theorem that this sentence is too short to contain.

[@unvergebeneid]

Nathan T And your document couldn't be exposed as nonsense despite years of trying? I highly doubt that to be honest.

[@ckmishn3664]

You can say it, but realize that KZbin comments don't record audio so we are very unlikely to hear you.

[@Jeff-jr4xw]

Love these early numberphile videos done on James’ bedsheets

[@numberphile]

Many of my chemistry videos, periodicvideos, have Brazilian Portuguese subtitles... Not for Numberphile yet I'm afraid!

[@Matthew-zy5sr]

hmmmm

[@hexagonist23]

If you're bored, and you have access to a pen and paper, a great way to pass the time is to do math. Like trying to manually calculate the first 50 digits of pi. Or reinventing all of math. Or proving Riemann's Conjecture. Or finding the first 100 digits of Grahams number. The possibilities are endless, and you just need some pen and paper, which kind of act like extended memory for your brain. Think of your mind as the RAM, and the paper as the hard disk.

[@josiewalz4124]

I’m amazed that he can just write on the perfectly white bed with a blue sharpie and no concern 🙌🙌

[@qpid8110]

I've come from the future year of 2021. Wikipedia says it is still not resolved xD

[@PMundi]

I really love these videos, the ones where you explain things such as this instead of just a single number are amazing and this is my fav. vid so far, keep up the great work :)

[@niboe1312]

You mentioned near the end that if the abc conjecture was proved, a lot of other stuff could be proven. What kind of stuff?

[@CreamyRootBeer]

YES! This is EXACTLY what I wanted them to add.

[@FrankHarwald]

& I'm interested to know whether there's some update on this problem. Specifically, whether there's someone who confirmed Mochizukis proof... :|

[@transformersguy234]

It's still being refereed I believe.

[@niceone4814]

Frank Harwald couple of mathematicians have confirmed it but theyre unable to properly explain/communicate the theory effectively. Most of the mathematics community are struggling/unbothered to learn a whole new set of complex mathematics to see if the proof is correct

[@maxschmidt1787]

.... so it seems that we have a new genius of the centuries on the earth surface?

[@captainpineapple5462]

that pigeon wallpaper though

[@RubyPiec]

4:06 "It's called the radical because it is welwiq-"

[@nilsr.k.7007]

‘It’s called the radical ‘cause it’s well wicked.’ I haven’t laughed as hard in quite some time

[@thedoublek4816]

Thank you very much, I couldn't understand all the words he said back then and was hoping to find a comment on that scene. And yeah, it also fkn killed me.

[@Yizak]

4:01 HAHA YES JAMES

[@air9music]

Rare to find shoegaze fans on math vids! 👋

[@spss76]

This is my fav channel on youtube

[@henryvalz93]

I love how you tested your sharpee by writing on your hand first. Do that all the time.

[@stupidmonkey151]

You guys should do a video on the Beal conjecture! That thing is hard!

[@deamn46]

congrats mochizuki!!!

[@sfratini]

Very explanation! Thanks.

[@iustinraznic5811]

I think this is my favourite conjecture so far ❤️

[@ianflanagan8744]

I have a mathematical conjecture, its stated like this: Let P be a prime number, P+1=n and let C be a different prime than P. given the equation (P^P)+n=C the gaps between the sizes of C become infinitely large but there are still infinitely many Cs that exist. examples (2^2)+2+1=7 (3^3)+3+1=31 (7^7)+7+1=823553 ect I call these solutions exponential primes.

[@liviu445]

why is this a conjecture exactly?

[@zeeshan008x52]

the best thing i have ever seen in youtube. it suits my taste.

[@shrinidhi111]

+Zeeshan Sayed Mohammed IKR

[@EebstertheGreat]

Note that the conjecture states only that there are finitely many coprime triplets (a,b,c) for which rad(abc)^k > c for _each_ k > 1. There are however infinitely many in total. As k approaches 1 from the right, the number of exceptions increases without bound, so that the union of all (a,b,c) satisfying the inequality for all k > 1 is infinite.

[@mikesnavy]

i cant stop shaking with joy after watching this video

[@uv206]

I know... a 4 year old video.. but, if you are watching, I have a question... What about increasing values of k? Does the number of "exceptions" decrease in some kind of regular way? Is there a large enough value of k above which there are no exception?

[@prosincr]

Jim Cross read the papers? It wasn't mentioned in the video, so there's only one other way.

[@JohnSmith-zq9mo]

Yes, if the conjecture is true then for some large enough value of k there are no exceptions. Quite easy to see actually. For k=2, for example, there would be finitely many exceptions only, if there are any. You can make each of these exceptions go away by increasing k, without adding any new ones.

[@danielnolan1591]

1+2=3 maths

[@jaredgarbo3679]

Both 2 and 3 have 1 as a factor. Sooo no bueno.

[@neonxd5062]

Jonathan Duffield Every number has 1 as a factor, since every number divided by 1 is the same number, so your '' no bueno '' isn't appropriate here...

[@looijmansje]

*Every whole number

[@o0TheKillerFish0o]

Jonathan Duffield 1 isn't a prime number, so it doesn't count.

[@tunachtumahgrowich222]

o0TheKillerFish0o You are right

[@anticorncob6]

When I was really little I thought algebra was actually letters as numbers, like when you ask somebody "What is t + 4?" and they say "Hold on...", start counting letters on fingers, and answer with "w" or "x" or whatever. When I learned letters were really substituting in numbers, it made so much more sense.

[@eiebsrebla]

‘Called the radical (changes accent) cos i’ is well wicked’. Love it

[@LazaroCarvalhaes]

Correction, dr James. The product (2 x 3 x 5 x 13 x 17) equals 6630 instead of 13260. You might have tapped "2" twice on your calc. Doesn't cancel the explanation though.

[@krisztian76]

There's another video like this, with this error.

[@AuroraNora3]

BRUUUUH turn on annotations you tw@

[@sastermodos886]

It's called the radical because its well wicked XD

[@diegoconnolly5317]

Why would you bother repeating something we all just watched?

[@sastermodos886]

Bro, when I posted this I was like 15, give me a break

[@delve_]

@Diego Connolly BECAUSE IT IS WELL WICKED

[@ruffifuffler8711]

It all depends on how you roll the wheelbarrow. If the handels are too low, you end up pushing it, but, if the handles are raised to the tipping point, it rolls by itself.

[@krinkovakwarfare]

This video needs WAY more views.

[@steeevealbright]

Ok not sure if this has ever been pointed out, but at 3:31 you multiply those numbers together and you DID THE MATH WRONG! 2x3x5x13x17 DOES NOT EQUAL 13260, it equals 6630

[@humanobject0.129]

OK, i ain't the only one who noticed this .

[@TheTexas1994]

All I noticed during this video was the weird pigeon wall paper

[@brucemoyle7610]

I really expected tortoises.

[@johnmorris9980]

Raising a prime number to a power is a short way to writing out repeated prime factors. So, for instance, the prime factors of 128 are 2*2*2*2*2*2*2. But since all of those are the number 2, you can just write it as 2^7. That also makes it easier to see the unique prime numbers, which you need for the radical bit of the video.

[@okinawapunter]

according to japanese newspaper asahi shinbun, Mochizuki's four IUTT papers will be published on a math journal, PRIMS, soon. so, presumably, IUTT papers passed referee's check.

[@kingkongtiger]

So.. Basically Shinichi Mochizuki developed some new technique/tools to solve this, and the community cant check his paper on the conjecture coz they dont really understand the technique in the first place?

[@cube2fox]

@@dalailamabama Stop pretending to know more than you know.

[@omikronweapon]

And here I was thinking doctors looked down on others. Thanks for proving me wrong...

[@cube2fox]

"moronic fuckwit" "dirty animal feces" 🤔

[@mrlagx]

@@cube2fox that escalated quickly

[@josephbrandenburg4373]

@@dalailamabama You don't have a Ph.D.

[@smittywerbenjagermanjensen7027]

Anyone else notice his thirteens can look like Beta

[@mastershifu2065]

His fours look like sixes to me

[@okinawapunter]

There is a lecture video by Mochizuki at MSRI in 1999, "The Hodge-Arakelov theory of elliptic curves".

[@maxschmidt1787]

Very interesting all this issue about abc conjecture. It reminds me very much of the Voynich Manuscript which nobody of the scientist really understands/could translate.

[@shampoable]

Shouldnt 2*3*5*13*17 = 6630? 13260 is 2*6630

[@namusmotorola8075]

I was rolling down to see if anyone, absolutely anyone has noticed, and I was getting dismayed. May be there are more, but you saved my life!

[@humanobject0.129]

@@namusmotorola8075 u aren't the only one who needed a life saver .

[@user-me7hx8zf9y]

yes

[@josephbrandenburg4373]

It sounded like he said "equals to" but I think he said "equals two."

[@adityaghosh3234]

I can solve it, but gotta go feed my dog.

[@kyzer422]

This is just really cool!

[@arslayah3169]

i cant do it myself, but when it says [inaudible] in the subtitles at 4:08 or around that, it should say "well wicked"

[@arcijsb3441]

2*3*5*13*17=6630

[@johannesh7610]

Indeed, he got a factor of 2 too much

[@user-me7hx8zf9y]

he was 2 excited, therefore doubling his answers

[@12Sangjin]

Brandon Koerner excellent

[@ItachiUchiha-ns1il]

Why is this being filmed in a bedroom?

[@bobsmith-ov3kn]

regarding whats show right before 4:00... This is only because you're taking unique primes, if you'd multiply all the 5's and the 2's (that you convientialy just wrote as exponents) you would always get a larger number

[@bobsmith-ov3kn]

bob smith seems pointless anyway, as this is at the heart of the "problem" of this conjecture. Only using one of each prime factor even if there are multiple copies of the factor (its a prime^power of something)is an arbitrary and useless function.

[@TheFailOrNot]

This is the first time KZbin subtitles worked ! It was enabled for some reason but it worked perfectly ! Either the subs got better or the guys from nuberphile speak a perfect English :D

[@abdullahyosof6041]

very cute wallpaper

[@General12th]

*BUT IS IT RIGHT??? * 2019 THE PUBLIC NEEDS TO KNOW

[@kinyutaka]

If you take the radicals and raise them to a power above one, then you are making them bigger than they were in a multiplicative fashion. As the examples get bigger, they increase exponentially. 5 to the power of 1.1 is 5.87, 10 to the power of 1.1 is 12.59. That tiny increase in exponent has a large effect. But c only grows by addition, and is unaffected by the exponent completely. That means that you have to be even more contrived to make examples where the radical of abc to the k is less than c itself, where with k equaling one, you can simply plug in c as some factor of 2 and b as some factor of 3, and produce infinitely many results where c is larger than the result.

[@mal2ksc]

That pigeon wallpaper, aagh! It had me thinking of Renton's bedroom in _Trainspotting,_ where his parents forcibly detoxed him.

[@mohamedtalaatharb2441]

5 Years later, and the proof hasn't yet been accepted. It is gonna take a while.

[@Chezmemes]

at 3:25, 2*3*5*13*17=6630, not 13260...

[@Ideophagous]

Chez Memes You're right. He probably multiplied by 2 twice. 6630*2=13260.

[@Chezmemes]

yeah, that let me rethink the accuracy of the rest of his videos...

[@Ideophagous]

Chez Memes It doesn't affect what he said about the conjecture actually.

[@Chezmemes]

that just raise the question whether videos are reviewed before publishing, and therefore whether other mistakes are present in other videos. Overall, that should not be many, but ...

[@alwinpriven2400]

Chez Memes he did place an annotation that says he did a mistake.

[@philosophy210creatio]

If you google "Invitation to Inter-Universal Teichmuller Theory," you can find a survey article written by Mochizuki on his work that tries to explain the ideas of what he did via analogies to other areas of mathematics.

[@remixener22]

a+b=c can be factored into x+y=z. Square it, you'll get d+e=f. Factorialize that and you get m+n=o

[@RedSkyHorizon]

Cuius rei demonstrationem mirabilem sane detexi. Hanc marginis exiguitas non caperet

[@anastasiadunbar5246]

englsh pls

[@RedSkyHorizon]

+Anastasia Dunbar It is the original Latin text from Pierre de Fermat which when translated means, ''I have discovered a truly remarkable proof of this theorem which this margin is too small to contain.''

[@anfiwa]

+Anastasia Dunbar get educated pls

[@Pattonator14]

+anfiwa lol because everywhere teaches Latin

[@ameyaparanjpe6179]

A+B=C Let's take 1 as 'A' Let's take 2 as B' 1+2=3 Therefore a+b=c All of them are whole numbers. It's proven!

[@mateuszdziewierz4234]

3²+4²=5² Fermat's last theroem solved! (A^n)+(b^n)=(c^n) for n=2 A=3 b=4 c=5

[@cube2fox]

For anyone interested in the status regarding a proof of the conjecture, there is a highly interesting (non-technical) article published in Quanta Magazine, it's called "Titans of Mathematics Clash Over Epic Proof of ABC Conjecture". It can be found via Google.

[@Jaburu]

the youtube-allows-links conjecture has long been proven

[@LoungeFly02]

I came on here to ask to do a video about Fermat's Last Theorem, but I saw that one of the top comments is already about that soo....I think I'll give that one a thumbs up too!

[@RedInferno112]

0:01 to 0:09, doesn't even look like equations. Doing A-Level Further Maths and thought I'd at least know what the basic concept of it is.... got a long way to go it seems.

[@koolguy728]

+RedInferno112 Even graduate level maths wont necessarily help you with any of that. It's a specialization of a specialization.. hes invented a sub-field essentially.

[@RedInferno112]

koolguy728 That almost takes away the beauty of maths

[@koolguy728]

RedInferno112 The beauty of anything is 100% subjective. It may be less beautiful to someone who can't understand it, but to him I'm sure its the most beautiful thing in the world.

[@RedInferno112]

koolguy728 True, I should have used a more defined term. My idea of maths was that it explained everything in the deepest, most simplistic and precise way possible.

[@RedInferno112]

aman verma So it would seem. Everything seems like it's just random unless you understand why.

[@Qermaq]

What if k

[@General12th]

Qermaq Then there are infinitely many exceptions, just as if k = 1.

[@violetlavender9504]

From Wikipedia, the free encyclopedia. In August 2012, Shinichi Mochizuki released a series of four preprints on Inter-universal Teichmuller Theory which is then applied to prove several famous conjectures in number theory, including Szpiro's conjecture, the hyperbolic Vojta's conjecture and the abc conjecture.[15] Mochizuki calls the theory on which this proof is based "inter-universal Teichmüller theory (IUT)". The theory is radically different from any standard theory and goes well outside the scope of arithmetic geometry. It was developed over two decades with the last four IUT papers[16][17][18][19] occupying the space of over 500 pages and using many of his prior published papers.[20] Mochizuki released progress reports in December 2013[21] and December 2014.[22] He has invested hundreds of hours to run seminars and meetings to discuss his theory.[23] According to Mochizuki, verification of the core proof is "for all practical purposes, complete." However, he also stated that an official declaration should not happen until some time later in the 2010s, due to the importance of the results and new techniques.[22] The first international workshop on Mochizuki's theory was organized by Ivan Fesenko and held in Oxford in December 2015.[24] It helped to increase the number of mathematicians who had thoroughly studied parts of the IUT papers or related prerequisite papers. The next workshop on IUT Summit was held at the Research Institute for Mathematical Sciences in Kyoto in July 2016.[25] After that workshop at least ten mathematicians now understand the theory in detail.[26] There are several introductory texts and surveys of the theory, written by Mochizuki and other mathematicians.[27]

[@jonavuka]

Numberphile the only channel to zoom in to faces at an uncomfortable level