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Show that an inverse of a modulo m. where a is an integer

Discrete Mathematics and Its Applications | 7th Edition | ISBN: 9780073383095 | Authors: Kenneth Rosen ISBN: 9780073383095 37

Solution for problem 8E Chapter 4.4

Discrete Mathematics and Its Applications | 7th Edition

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Discrete Mathematics and Its Applications | 7th Edition | ISBN: 9780073383095 | Authors: Kenneth Rosen

Discrete Mathematics and Its Applications | 7th Edition

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Problem 8E

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.

Step-by-Step Solution:

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

=>

Step 2 of 2

Chapter 4.4, Problem 8E is Solved
Textbook: Discrete Mathematics and Its Applications
Edition: 7
Author: Kenneth Rosen
ISBN: 9780073383095

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Show that an inverse of a modulo m. where a is an integer