Multiplicative Inverse of 3 (mod 26)

[@kirstensee6459]

please add brackets when you're arranging/evaluating the terms on the left!

[@NathanStraub92]

I’m practically crying thank you

[@MathsWithJay]

You're welcome!

[@stuartmeadowcroft1802]

Thanks for the straightforward video - more tutors need to realise that you need to start with the simplest possible example!!

[@MathsWithJay]

Glad it was helpful!

[@isnintendo8656]

this video is the best so far. excellent explanation!!

[@MathsWithJay]

Wow, thanks!

[@supremepizza2267]

i am kind of confused where the 9 cam from at about 5:12, if you added 3 + 8, doesn't that equal 11??

[@MathsWithJay]

No! ... 3 + 8 x 3 = 1 x 3 + 8 x 3 = (1 + 8) x 3 = 9 x 3

[@aeiou1303]

I can't understand where 9 came from in =9x3-1x26

[@MathsWithJay]

At what time in the video?

[@huicheng9160]

bruh theres a 8x3 in the back, so she combined the 3s, making 9x3.

[@luckywitch0128]

I'm trying to use this method for MI of 2 mod 9 and am just absolutely lost. I only get one formula so I can't do the substitution part of this

[@kaursingh637]

my lord whether we will find modulo maths in discrete maths book ? or number system book ?

[@MathsWithJay]

I teach this as part of number theory

[@axeldiaz7960]

Hello! Really appreciate the video! Does this mean that if 7 and 24 weren’t comprime, there would be answer? Because there would be no v and w such that 7v + 24w = 1?

[@MathsWithJay]

There would be NO answer

[@Reedz22]

how you get 9 x 3 - 1 x26?

[@MathsWithJay]

3 + 8 x 3 = 9 x 3 and the - 1 x 26 is the same as the previous line. Does that answer your question about 5:24?

[@MathsWithJay]

3 + 8 x 3 = 9 x 3 and the - 1 x 26 is the same as the previous line. Does that answer your question about 5:24?

[@musteroogway6962]

Where did you get 9?

[@MathsWithJay]

3=1x3 and so altogether we have one plus eight lots of 3, so nine.

[@manu-mm4pc]

I dont see how 3-1X(26-8X3) give 9X3...

[@joshuawalfall]

This was a great tutorial, thank you

[@MathsWithJay]

You're very welcome!

[@maherriyadh5647]

3v = 1 - 26y , where did you get 1 from ?

[@MathsWithJay]

@Maher Riyadh: The right hand side of the congruence is "1".

[@HakarDoski]

5:16 how did you know that 1 is 9 times 3?

[@MathsWithJay]

Because in mod 26, 27 is equivalent to 1

[@HakarDoski]

@@MathsWithJay if I use 7 does the algorithm become? 26 = 3x7 + 5 7 = 1x5 + 2 5 = 2x2 + 1

[@MathsWithJay]

Yes...can you continue to do the next stage?

[@HakarDoski]

@@MathsWithJay nooo, that's where I'm struggling, I know it becomes: 5=26-3 *7 2=7-1 *5 1=5-2 *2 and 1=5-2*(7-1*(26-3*7)) but after that, I don't know what happens

[@MathsWithJay]

Do it step by step: 1=5-2*2 1=5-(7-5)*2 1=5*3-7*2 1=(26-3*7)*3-7*2 ....Now write this so it is 1 = a combination of multiples of 26 and 7

[@yifuxero9745]

Multiplicative inverse of 3 mod 26, no problem. Write out the continued fraction representation of 3/16 = [ 8, 1 2] Underneath write the convergents [1/8, 1/9, 3/26]. The answer is the denominator to the left of the 26, = 9 since 3 * 9 = 1 mod 26..

[@MathsWithJay]

Why not make a KZbin video to explain this?

[@yifuxero9745]

Thx, I'll try to get all of the instructions into one paragraph.

[@iHaCKeRXZ]

Thanks , i did it with 7 mod26 (it's 15) and i ended with this : 3x26-11x7 . so what should i do with the -11 .

[@MathsWithJay]

Add on 26 to get 15. Does that make sense?

[@boudortest]

@@MathsWithJay excuse me but why ?

[@MathsWithJay]

@axel ava: In mod 26, -11 is congruent to 15 (and -11 + any multiple of 26 ).

[@khoadiep3774]

so how can we find the inverse of 26 (mod3) ?

[@MathsWithJay]

How do you think you would start on this?

[@zahidhasanmozumder1075]

I think that will be 3v = 26w + 1 instead of 3v = 1 -26w

[@MathsWithJay]

Your w will have the opposite sign to mine...so it will still work

[@farnazjalili5620]

Why this doesn't work for 13?

[@MathsWithJay]

@Farnaz Jalili: 13 in place of 3, 1 or 26?

[@farnazjalili5620]

@@MathsWithJay in place of 3. thanks

[@MathsWithJay]

@Farnaz Jalili: Because 13 and 26 have a common factor (13). If 13v is congruent to 1 (mod 26) then 13v=1+26k where v and k are integers, so 13v-26k=1 or 13(v-2k)=1....this is impossible because the left hand side has a factor of 13, but the right hand side does not.

[@muellerhans]

This with 7 would be interesting. Since I don't get 1 on the left side for backwars substitution but 2.

[@MathsWithJay]

@Hans ... 7 instead of what?

[@muellerhans]

@@MathsWithJay 3. So 7 mod 26.

[@MathsWithJay]

@Hans...so you want to solve 7v congruent to 1 (mod 26) The first part needs to be continued until you get a "1", so there will be three lines of working before you start backwards substitution...the third line will be 5=2x2+1

[@CodingJesus]

@@MathsWithJay 26 = 8 * 3 + 2. 7 = 2 * 3 + 1. Where did you get 5 = 2 * 2 + 1?

[@billygraham5589]

Uh... I may not know what I am talking about, but it appears that the multiplicative inverse of 3 (mod 26) would be 35. I say this as 3(9) = 1(mod 26) >>> 26 + 9 = 35 >>> 3 x 35 = 105 >>> 105 -:- 26 = 4 R 1 >>> therefore 35 = the multiplicative inverse of 3 (mod 26). I saw this method on another video, and I don't fully understand it, but I do somewhat understand it, and I can see that 3 x 35 brings you to "1" on the mod 26 "clock." Yes???? What do you think? So what are we being taught in this video? Seems we are being taught to solve Bezowt's Theorem, but not actually being taught to come up with the multiplicative inverse of 3 (mod 26).

[@yuanshi269]

How do you know that it is nine from the fourth solution?

[@MathsWithJay]

At what time in the video?

[@yuanshi269]

@@MathsWithJay 5:18

[@MathsWithJay]

3+ 8x3 = 9x3 because 1+8=9

[@yuanshi269]

@@MathsWithJay thank you that helped me a lot

[@vlamz7419]

how do you find the multiplicative inverse of 2

[@MathsWithJay]

@jongdream: If you work through the same method as shown in the video, you would get 2v + 26w = 1 where v and w are integers, so the LHS of this equation is even and the RHS is odd, showing that it is not possible to find a multiplicative inverse of 2 in mod 26.

[@amriohm]

Thank u a that’s helpfull 🙃❤️

[@MathsWithJay]

You’re welcome 😊

[@harshberiwal7200]

Though, the video was great. Thanks

[@MathsWithJay]

@Harsh: Thank you!

[@yifuxero9745]

Here's an easier way; With your pocket calculator write the partial quotients of 3/16 = [8, 1, 2]. Underneath, write the convergents = [1/8, 1/9, 3/27]. The answer is 9, the denominator to the left of the rightmost fraction. Rules apply to a mod n where n > a and gcd (a, n ) = 1. Rules differ slightly if you get a continued fraction with an even number of partial quotients. Example: Find 3 mod 58. As before, the partial quotients are [19, 3] and underneath we have [1/19, 3/58]. In the case of an even number of partial quotients, take the difference of rightmost and next denominator to the left = (58 - 19) = 39. Correct since 3 * 39 = 117 which is 1 mod 58.

[@MathsWithJay]

Why not make a KZbin video to explain this?

[@floatingyunsan]

Where did the 9 come from 🤦🏻‍♀️ahhh thi s is too hard

[@MathsWithJay]

At what time in the video?

[@azumamurakami7842]

3X=1 mod26 then 29X=1 mod26 --------(1) -23X=1 mod26 --------(2) (1) + (2) 6X=2 ----------(3) (3)X4 + (2) X=9 mod26 Ans. 9

[@MathsWithJay]

Interesting

[@omonotahustle3493]

he won't pin this, *how did you get 9 ?*

[@MathsWithJay]

3 + 8 x 3 = 9 x 3 because 1 + 8 = 9

[@IshangKumar]

please moan my name in next video.... really lovely voice

[@MathsWithJay]

user-no7mm9en4s is a long name...

[@That_Singing_Nurse_Dude]

um what

[@MathsWithJay]

at what time in the video?

[@tom-pd2uk]

ty for this still didnt help our lesssssson

[@MathsWithJay]

do you have a similar question to do?

[@harshberiwal7200]

Typical British accent

[@MathsWithJay]

Harsh!

[@anayaggarwal6877]

Not very helpful

[@MathsWithJay]

Do let us know if you can recommend another video

[@jerrymahone335]

if she has to explain this to you stop now. you will be totally lost in DES, AES, RSA, and EC maths. the discrete logarithm problem. cryptology is for mathematicians.

[@MathsWithJay]

@Jerry: I guess everyone has to start somewhere!

[@jerrymahone335]

@@MathsWithJay she did make this problem harder than it needed to be. the 26 and and mod 26 cancel out leaving you with 9 (3) = 27. 26|27 = 1.038461538, subtract 1 and multiply the difference by 26. that is congruent to 1 modulo 26. I believe her showing off was what confused you. you generally keep the problem intact to get the s and t values i.e. the Eigenvalues or Eigenvectors, or the multiplicative inverses. explain why you have have a product of 1 to have a multiplicative inverse. give some kind of proof when you making a statement. this is where you start.

[@trollfack2966]

Can you explain why the reciprocal modulo can't be 2,4,6 or 13?

[@MathsWithJay]

At what time in the video?

[@trollfack2966]

@@MathsWithJay it's not in the video but I couldn't work it out

[@anishakundu4851]

Because 2 and 26 are not relatively prime ig