   Chapter 8.4, Problem 35ES ### Discrete Mathematics With Applicat...

5th Edition
EPP + 1 other
ISBN: 9781337694193

#### Solutions

Chapter
Section ### Discrete Mathematics With Applicat...

5th Edition
EPP + 1 other
ISBN: 9781337694193
Textbook Problem
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# Corollary 8.4.7 guarantees the existence of an inverse modulo n for an integer a when a and n are relatively prime. Use Euclid’s lemma to prove that the inverse is unique modulo n. In other words, show that if s and t are any two integers whose product with a is congruent to 1 modulo nm then s and t congruent to each other modulo n.

To determine

To prove:

Any two integers whose product with a is congruent to 1 modulo n are congruent to each other modulo n.

Explanation

Given information:

aand n are relatively prime.

Proof:

Suppose a,n,s,s' are integers such that as=as'1(modn).

Consider the quantity as's.

as's=(as')s=(as)s'by the associative property of integers

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