Modular Exponentiation (Part 1)

[@mahdi-hasan]

49*(-7) = -343

[@akash_assist]

49 mod 30 is 19 ........and then you multiply 19 by -7 and you get -133.

[@armanlalani]

For those who are still confused - 23³ mod 30 = (23 x 23 x 23) mod 30 In the prev video, we saw the property - (a mod n x b mod n) mod n = (a x b) mod n Using this property of modular arithmetic from the previous video, we get = [23 mod 30 x 23 mod 30 x 23 mod 30] mod 30 Now, since we know 23 mod 30 = 23, thus (23 x 23 x 23) mod 30 = 12167 mod 30 = 17. Alternatively, we can also substitute 23 mod 30 with -7 mod 30 which makes the calculation simpler and which is also done in the video. = [-7 mod 30 x -7 mod 30 x -7 mod 30] mod 30 Again using the same property of modular arithmetic, = (-7 x -7 x -7) mod 30 = (-7)³ mod 30 = (49 x -7) mod 30 Again using the property - = [49 mod 30 x -7 mod 30] mod 30 = [19 mod 30 x -7 mod 30] mod 30 = (19 x -7) mod 30 = -113 mod 30 We see 49 x -7 mod 30 would give -343 mod 30 = 17 (since -343+30x12 = 17, to make -343 positive we had to add 30 twelve times which yielded 17). But 49 was simplified to 19. The properties of modular arithmetic have been used implicitly to make the calculation easier.

[@hivirupalihena3102]

Thanks, This helped than the video

[@MaheshKumar-vi7pi]

So you used commutative property and taken both A= 23, B=23. How?

[@simayturgut]

thanksssssssss

[@awasthi_108]

thanks broooo

[@foxdeveloper7707]

Great comment :)

[@oshikkhittt]

Hello Neso Academy,I really highly applaud you👏 for making this modular exponentiation a simply but perfectly explained one😍.❤From Bangladesh.And also my endless thanks🥰☺

[@Dedo12362]

bangladesh cricket team is not good

[@lindeanchuang8115]

Thank you very much. Your explain is much easier understand than my text book.

[@avocadorable_s5637]

Wow, i spend 2 hours trying to understand my lecturer's notes on modular exponentiation, even went through so many web tutorials, and still wasn't clear. This one single video just made me understand the whole concept in 10 min. Great!!! Thank you so much for the clear and concise explanation!!!

[@chaffylocket1174]

hello how did 49*-7mod30 become -133mod30

[@lingeshwarans8756]

He use reminder value of (49 ÷ 30 = 19) and 19 * 7 = 133

[@sabinomuniz5542]

Thank you, you explained it much simpler than my learning material!

[@rohitsharma7553]

Can you provide us the whole syllabus of this course or the length of this course with roadmap

[@adiba-cse-22]

You have explained it in the most easiest version. Thank you.

[@chaffylocket1174]

hello how did 49*-7mod30 become -133mod30

[@davidsalasmerino7185]

Thank you, I didn't catch it well the modular exponentiation, but with ur video I uderstand it!!!

[@KenPoke-cz2je]

For example if the mod is 284 so how can you calculate it ? Every time you made it as 1 of course easy to calculate

[@sonikaur2718]

Thanks sir 🙏 the way you explain the things is splendid 👌 👏

[@ogboota8032]

This video gave me a booster,.. thank you 😎🙏💐

[@itsoknottobeok9381]

I'd appreciate if u take the next dose too

[@youngcoders1437]

how can 49*7= 133 instead of 343???

[@sammuriithi1313]

exactly!!!!!!!!

[@nuhusherif5063]

@@sammuriithi1313 he skipped the part that was supposed to be (49 mod 30)=19 multiplied by ( -7 mod 30). so then (19 x -7 ) mod 30 = -133

[@Sanastamen]

This is really helpful.

[@lingeshwarans8756]

He use reminder value of (49 ÷ 30 = 19) and 19 * 7 = 133

[@PraveenKumarK-y9o]

In the calculation there are errors 23^3 mod 30, in the fifth step its -343 mod 30 and error in the calculation 11^7 mod 13 there is an error in the fourth step

[@vladfishistaken]

it not a mistake he just simplified the expression, instead of 49*-7 mod 30 he did (49mod30 / which equal to 19)*-7mod30, result is exactly the same

[@isirlasplace91]

I love the way you explain!!! Way better than my current professor!!!😁💕

[@I_just_love_ps]

the thing is not with your professor, it's that when you was in the school you was tired or not consentrated so that it came difucile by the way i am not a teacher

[@emreproxtr]

​​@@I_just_love_psyou don't have to have good teaching skills to be a professor. Most professors are really bad at teaching because they aren't trained for that. Nesoacademy has valuable "teachers"

[@xboyPToficial]

Sorry guys? -133 mod 30 = -13. COuld you please explain? Thanks

[@andrewporter1868]

Good video, but you need to put parentheses around negative bases to avoid ambiguity. Otherwise, it is parsed -(7^3).

[@socraticmathtutor1869]

I was just about to say that :)

[@mrtopaz5830]

saving me thank so very much

[@soniajadhav8438]

Hello sir can you do video on RSA algorithm plz 🙏🏻

[@Cuồng-Vương-2]

Great 😍

[@rakesh9149]

How is 23 mod 30 is equal to -7 mod 30 ?

[@mohamedfathy002]

you can subtract 23 by 30 which is -7 and -7 mod 30 gives the same result

[@klemo2529]

49 * -7 (mod 30) = -11 * -7 (mod 30) = 77 mod 30 = 17

[@carterschmidt7411]

How did you get -11?

[@klemo2529]

@@carterschmidt7411 if adding x in mod x lets the number be the same, then subtracting x should also keep the number the same 49 - 30 = 19, and 19 - 30 is -11 so 49 = -11 mod 30

[@benjaminrutto8365]

atleast yours is better than that -133 i didnt get that calculations

[@momotarodadumpling4065]

@@benjaminrutto8365 yeah, I too didn't understand that

[@anzatamveel1761]

But what if it is 2015^17mod 3233 ? My problem is still didn't solve

[@ashaay5832]

Thank you so much buddy ❤

[@varunswamy5813]

umm just a update 49 * -7=-343

[@harshitabhradwaj4279]

49 mod 30 is 19 ........and then you multiply 19 by -7 and you get -133

[@lingeshwarans8756]

He use reminder value of (49 ÷ 30 = 19) and 19 * 7 = 133

[@bindiyakirlaya8657]

Thank you so much

[@underes]

49×7 = 343 . I don't know which math you are teaching but explain it...

[@nibbanews3472]

even i got confused for a min.

[@worldnewsvideos]

same

[@anuragdubey285]

30×11= 330 So reminder is -13 17 Answer is correct

[@princepatel6645]

49-30= 19 (49 mod 30) 19*7 = 113

[@thirumalaivasanc1752]

@@princepatel6645 crt bro

[@sammuriithi1313]

49*-7 = 133 ? am i tripping or sth?

[@vladfishistaken]

49mod30=19, 19*-7 = 133

[@meetpatel1032]

How to solve (5)^15 mod 23 ?

[@pavel1689]

at 4:11 i think 49*-7 = -343

[@Utkarshkushwaha-ld8xh]

Yes you are right 👍

[@pavel1689]

@@Utkarshkushwaha-ld8xh All the best for your exam.

[@SawairaBilal-u2j]

And for bigger like 1816^13 mod 2437

[@juancarlosrosalesc.9937]

how does -2 seven times is equal to -128?

[@robertholder]

-2 * -2 * -2 * -2 * -2 * -2 *-2 = -128 maybe you were thinking he -2*7 ?

[@ColdFuse96]

Thank you so much!!!!

[@mustafaimam8677]

how did you get -7????? for 23

[@fitrafep]

-7 === -7 +30 === 23 mod 30

[@kranthiboggu2177]

Not specified perfectly. Very bad calculation. Calculations not explained

[@mac2105]

Writing -1^329 triggers my OCD, please write (-1)^329 thanks ;)

[@gusionfusion1073]

49 * -7 mod 30 = -113 mod 30 how it came can any1 explain?

[@maxwellconniff1189]

Here's an informal way to do 49 * -7mod30 = -113mod30 49 * -7 = -343 Thus: -343mod30 and now we have to simplify/reduce If you recall from neso's earlier video on modular arithmetic in the part covering congruence: If a is congruent to b(modm) then a = km+b In practice this means that for any integer 'k': -343mod30 = (k(30) + (-343))mod30 so choosing k = 7: -343mod30 = (210 + -343)mod30 = -133mod30 However, I think it's easiest to just choose largest k such that km is still less than |b| i.e. choose largest k so k(30) < 343 k=11 -343mod30 = (330 + -343)mod30 = -13mod30 Hope that helps.

[@potatootter5088]

@@maxwellconniff1189 Hi, where did you get 7 = k? From -7? How did it change to +7 then? Thanks.

[@galibkiyaadein4627]

This was mistake just leave it and do calculation on your own 🙃

[@plexradio]

Thumbs down. No proper explanation on how 47 * -7 = 133. Garbage

[@shonadevgan7885]

-7 * 49 mod 30 = -133 mod 30 49 mod 30 = 19 So 19 * -7 mod 30 = -133 mod 30

[@aaryan1143]

You Should Explain The Calculations In a Better Way, Rest Of It is Good!

[@azkaatique2874]

38*8 mod 63 how can find

[@bhimmu-uj6lb]

can I do like this : 31^500 mod30 =(30+1)^500 mod 30 ; [30^500+2*30*1+1^500] =mod30 ; =30^500 mod 30+60 mod30+ 1mod30 0+0+1mod 30 =1mod30; 1/30 =Q=0+R=1 =1

[@vinodbarti9237]

2 pow 343 mod 142 will be

[@monicabattacharya6416]

please complete Java programming tutorials as soon as possible 🙏🏼

[@rajeshprajapati1851]

Why so demanding ?

[@monicabattacharya6416]

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[@monicabattacharya6416]

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[@rajeshprajapati1851]

@@monicabattacharya6416 OK

[@anurag-pathak10]

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[@AFriend9902]

-7 *-7 =+49?

[@gauravaghariya]

Can anyone solve 2^(62)mod77=?

[@manishapanda5770]

49 x 7 = 343 ?

[@ramyabotha1876]

sir do for 176 power 23 mod 187

[@adinapunyobanerjee9481]

Why?

[@spyxxer8849]

@@adinapunyobanerjee9481 Because it seems this is not foolproof

[@pavan.b9881]

Sir how got -13

[@Lola-mc7tt]

Thank you very much 😊

[@arpitadey3643]

example 1-------->>>> (49*(-7))=133 how?

[@ngocjenny6106]

so, he did 49 mod 30 first, which equals 19, and then he multiplied 19and -7 and got -133 honestly, it took me a bit to figure out, but since he doesnt want us to use a calculator, he just did it this way

[@bubblebath2892]

how can 23 mod 30 be -7 ??

[@sejalsanjaybhattad3354]

Please Upload Steam and Block Ciphere

[@rajeshprajapati4863]

I think it is available on website.

[@jainakash24]

He needs a calculator to do 49*7😂

[@MarutiBhakth7147]

4:10 -7 * 49 = 133 ?? how

[@Lola-mc7tt]

Good luck

[@pushpdantpurigoswami]

What answer if 14^27 mod 55 !!?????? You solve easy example try hard And prove your mind !...

[@Whimsy_Artisan]

Sir please next video upload kijiye

[@riyam967]

can anyone explain to me logic behind having -7 as a result of 23 mod 30

[@MrBlancify]

23 = 30*0 + 23 or you can have 23=30*1-7.

[@MaheshKumar-vi7pi]

@@MrBlancify That is a very relevant solution. Thanks Can you tell how to know that there are only 02 possible solutions of the 23 mod 30? Can’t there be more solutions?

[@MrBlancify]

@@MaheshKumar-vi7pi Techincally infinite solutions. It could be -277 for example, 23 = 30*10-277. But the solutions we want in modulo are ones closest to zero.

[@MaheshKumar-vi7pi]

@@MrBlancify Thanks Man. Great explanation.

[@MaheshKumar-vi7pi]

@@MrBlancify -7 is closest to 0 than 23 itself, hence we go with -7? Right?

[@matheshwaran4028]

find the value of 6^24 mod 35 using exponentiation

[@matheshwaran4028]

How sir

[@GreyJaguar725]

​@@matheshwaran4028I think that if you write 6^24 = 6^(2*12)= (6^2)^12=36^12 Since 36 = 1(mod35) Then 36^12(mod35) = 1^12(mod35) =1(mod35)

[@babujimitra7920]

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[@陈妖精]

It's 16K views now.

[@ramankumar2666]

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[@rajeshprajapati1851]

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[@indogreek5565]

Sir, if you are teaching for free. Then how did you get money to eat.

[@rohitsharma7553]

1) There are a lot of good students who support these organization by donating some money. 2) This academy also make some money from KZbin. 3) There are some paid courses that are only available on nesoacademy website from there they also make some money. That's how they get money to eat.

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[@harismuhammad2099]

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[@sweetgirlllll]

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