Number Theory | Linear Congruence Example 2

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Күн бұрын

Пікірлер: 69

@poppycock3954 3 жыл бұрын

Almost every video I've seen so far has had a different explanation... so far I think this one makes the most sense for me, thank you!

@victorvalenciasanchez6756 3 жыл бұрын

ikrrrr

@sarazahoor9133 3 жыл бұрын

Same here!!!

@FiGHTxANIME08 3 күн бұрын

Hey bro where are you from

@meaty1702 Жыл бұрын

I understand how the inverse part can be a bit tricky for people to understand, since he did not explain it very clearly, so I'll show you how you can think instead. When you come to the part of 5x congruent to 2 for mod 9, imagine the list of numbers that 2 could be instead of 9. By adding 9 to 2 repeatedly, you'll get said list. The list you get is 2, 11, 20, 29, 38.... Here you see that 20 is divisible by 5, such that we can get that 5x/5 is congruent to 20/5 for mod 9, which is equal to x congruent to 4 for mod 9, and there you have your answer.

@DavisMaths Жыл бұрын

Is there a way that we don’t need the trial and error method?

@meaty1702 Жыл бұрын

@@DavisMaths I am not sure, but this is the method that I found to be the easiest to understand. It's not that difficult if you just write out the list. I did not understand congruence until the idea of lists was mentioned in some youtube video I saw. You can think of it like this, if you have a congruent to b for mod n, the list will be {b, b+n, b+2n, b+3n, ....} This method is useful since it can also be used for squares. For example, if x^2 is congruent to 56 for mod 8, we know that you can not take the square root of 56. But if we write out the list: {56, 64, 72, 80, ...}, we find almost immediately that 64 is a square, as such we can take the square root on both sides and find the answer for x. Hopefully this explanation suffices. Goodluck!

@pushpalathadabburi8746 11 ай бұрын

Understood

@cjnadance7773 9 ай бұрын

This is also my strategy for solving such congruences. :) I thought I am the only one who makes use of listing the elements/numbers in b(mod n)

@richard-1604 2 жыл бұрын

I’m a retired life long learner who has always been interested in maths and number theory/math Olympiad problems is my current buzz. These videos are really great for bringing out the big points that might get missed with self study.

@wobblyjelly345 2 жыл бұрын

Yes I found the same, it can make all the difference. :)

@maxzriver 3 жыл бұрын

140x = 56(°252 ) simplificando 5x = 2(°9 ) 5x = 20(°9 ) x = 4(°9 )

@ocnhim8354 8 ай бұрын

bro looks jacked.. i think bro's worth listening to

@MoyoOpeolu 2 ай бұрын

😂

@georgesadler7830 3 жыл бұрын

Professor Penn, Thank you for a brilliant example on Linear Congruence.

@noahrubin375 3 жыл бұрын

For sure the best explanation out there!

@jaxsharp Жыл бұрын

u gotta be capping, his explanation was trash

@crossugo5738 2 жыл бұрын

The inverse part was a bit rushed, but this video is one of the best on congruences so far. Thanks a lot!

@cmfcf7180 2 жыл бұрын

what does the inverse bit mean pls?

@HanksJ62 2 жыл бұрын

Best explanation so far

@farihasifat 2 жыл бұрын

Much much-needed information is covered. Thank you so much.

@samueldeandrade8535 8 ай бұрын

Hahahaha.

@holyshit922 11 ай бұрын

Two ways of finding inverse 1. Eulers theorem 2. Extended Euclid's algorithm Extended Euclid's algorithm is more efficient

@samueldeandrade8535 8 ай бұрын

Man, just try some numbers first.

@jarrydbrennan286 4 жыл бұрын

BRILLIANT! Thank you for helping me see it

@vaggelismanousakis6147 8 ай бұрын

what do we do when the number 56 is raised in a very high power ? For example I was given this one: 8x ≡ 11^41 (mod 51) but I can't figure out how to solve it.

@S2KEVIN 3 жыл бұрын

Michael Penn, clutchhhhhhh

@Meenimie 9 ай бұрын

Why didn't he give the link to the previous video he mentioned?

@sonukumarnirala6896 Жыл бұрын

Nice explanation

@PunmasterSTP 3 жыл бұрын

I think this video was...modul-awesome! Thanks again for sharing.

@amaliacoughlan7071 4 жыл бұрын

Thanks man!

@pramod1159 5 ай бұрын

TF zuckerberg explained us this easily

@gegiojonjongegio7998 3 жыл бұрын

I don't really get why there are only 28 solutions, I mean, if you say x=4+9*53 for example it still works

@briana5708 3 жыл бұрын

You are right. There are infinite many solutions but only 28 unique solutions mod 252.

@gautamwarvatkar2778 Жыл бұрын

Ttooo good both the maths and the back ❤❤

@joseph-ianex 8 күн бұрын

So much good information, unfortunately my brain blew up, I'll try this video again after I master the fundementals more.

@sunr8152 Жыл бұрын

Perfect example.

@sukanyajha3675 4 жыл бұрын

like the way u teach 🤘🤘🤘🤘

@bolleholle 3 жыл бұрын

Why are there not infinite solutions of the form x=4+9n?

@RexxSchneider 2 жыл бұрын

There are. But after n=27, i.e. x=247, the next one is x=256 and that is the same as 4 (mod 252) and we go round the same set of 28 numbers differing by 9 each time. Remember we are solving 149x ≡ 56 (mod 252), so any of the infinite number of solutions will always reduce to the same set (mod 252). It is trivially true that all linear congruences (mod m) which have a solution x will have an infinite number of additional solutions that are congruent to x (mod m), so we conventionally only bother to record the solutions x that lie in the range 0

@juanroldan529 4 жыл бұрын

There won't be more modular arithmetic videos?

@dr.nobody3357 Жыл бұрын

This video is awesome.

@ThruGod233 Жыл бұрын

dont get the inverse part man

@uzytkownik9616 Жыл бұрын

Inverse (mod 9) has an analogy to rational numbers e.g. (1/2)*2=1 so if you multiply a number by its inverse you get 1. The same situation with (modulo 9). 5*2=1 because 5*2=10 and 10 gives remainder 1 by dividing by 9. That's why 5^(-1)=2

@samueldeandrade8535 8 ай бұрын

@@uzytkownik9616 you are a friend, friend.