   Chapter 8.4, Problem 25ES ### 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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# Use Theorem 5.2.2 to prove that if a and n are positive integers and a n − 1 is prime, then a = 2 and n is prime.

To determine

To prove:

When aandn are positive integers and an1 is prime, then prove that a=2andn is prime.

Explanation

Given information:

aandn are positive integers and an1 is prime.

Formula used:

Know that the factorization is (an1)=(a1)(1+a+a2++an1).

Proof:

Know that, (an1)=(a1)(1+a+a2++an1)

It is given that, an1 is prime.

So, a1=1or1+a+a2++an1=1.

Here, aandn are positive integers. Thus, a=2.

To show that n is prime, assume that n=mp for some integers m,p>1

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