Problem 8E

Show that an inverse of a modulo m. where a is an integer and m > 2 is a positive integer, does not exist if gcd (a, m) > 1.

Solution

In this question we have to show that an inverse of a modulo m. where a is an integer and m > 2 is a positive integer, does not exist if gcd (a, m) > 1.

Step 1

Here we use the method of contradiction

Let there be an integer x.

Such that

So , it means that there exists an integer j such that

=>