Question

Find an inverse of 16 modulo 17. That is solve 16x=1(mod 17)

Answer 1

Answer:

-1 is the inverse of 16 modulo 17.

Step-by-step explanation:

To find : An inverse of  16 modulo 17 i.e. $16x=1(mod 17)$?

Solution :

First we find the GCD of (17,16) using Euclid's algorithm,

$17=16\times 1+1$

Remainder is 1.

Which means, GCD(17,16)=1

Using back substitution we get,

$1=17-16(1)$

$\Rightarrow 16(-1)=1+17(-1)$

$\Rightarrow 16(-1)=1(\mod 17)$

i.e. -1 is the inverse of 16 modulo 17.

On comparing with $16x=1(mod 17)$

The value of x=-1.