Find the multiplicative inverse of 19 with 26 (under mod 26)

[Guest]

I am looking for this solution and tried to solve this on my own but I can't..
This is the problem in which we are using the Extended Euclidean Algorithm.

Can someone please solve this and illustrate a few steps that would be so helpful.

I am a guest but I will keep track of what's going on here in this thread. Any help will be appreciated.

[Guest]

Anyone Intersted???

[Guest]

I do not get what you want.
Multiplicative inverse is [tex]\frac{1}{19\times 24} = \frac{1}{494}[/tex]

[Guest]

I do not get what you want.
Multiplicative inverse is [tex]\frac{1}{19\times 24} = \frac{1}{494}[/tex]

Wanted to calculate Modular Multiplicative Inverse of 19 mod 26
This can be calculated using an extended euclidean algoritm. But I am unable to calculate it for 19.

i.e Inverse of 1 mod 26 is 1
The inverse of 11 is 19 and for 19 is 11.

[Guest]

You want to find x such that 19x= 1 (mod26).

That means that 19x= 1+26y for some integer y. We can write that as 19x- 26y= 1.

Now, the Eucllidean Algorithm: 19 divides into 26 once with remainder 7: 26- 19= 7.
7 divides into 19 twice with remainder 5: 19- 2(7)= 19- 2(26- 19)= 19(3)-26(2)= 5. 5 divides into 7 once with remainder 2: 7- 5= (26- 19)- (19(3)- 26(2))= 26(3)- 19(4)= 2. Finally, 2 divides into 5 twice with remainder 1: 5- 2(2)= (19(3)-26(2))- 2(26(3)- 19(4))= 19(11)- 26(8)= 1.


So one solution is x= 11, y= 8.

The multiplicative inverse of 19 (mod 26) is 11. 19*11= = 209= 8*26+ 1=1 (mod 26).