   Chapter 8.4, Problem 42ES ### 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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# According to Fermat’s little theorem, if p is a prime number and a and p are relatively prime, Then a p − 1 = 1 ( mod   p ) . Verify that this theorem gives correct results for the following: a = 15       and       p =7 a = 8     and       p =11

To determine

(a)

To verify:

Fermat’s little theorem gives correct results for a=15 and p=7.

Explanation

Given information:

a=15 and p=7.

Concept used:

According to Fermat’s little theorem, if p is a prime number and a and p are relatively prime, then ap1=1(modp).

Calculation:

It is given that a=15 and p=7

15=2×7+17=1×7+0

So the GCD of (15,7)=1

Since the last remainder in the division is 1

To determine

(b)

To verify:

Fermat’s little theorem gives correct results for a=8 and p=11.

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