Multiplicative Inverse of 3 (mod 26)

How to use Euclid's Algorithm to find a multiplicative inverse of 3 (mod 26)

[kirstensee]

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

[stuartmeadowcroft]

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

[isnintendo]

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

[supremepizza]

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

[luckywitch]

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

[aeiou]

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

[kaursingh]

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

[HakarDoski]

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

[yifuxero]

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..

[axeldiaz]

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?

[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 .

[khoadiep]

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

[maherriyadh]

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

[zahidhasanmozumder]

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

[vlamz]

how do you find the multiplicative inverse of 2

[billygraham]

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).

[yifuxero]

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.

[muellerhans]

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

[yuanshi]

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

[floatingyunsan]

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