Answered: give a counterexample: 1. The integer…

give a counterexample: 1. The integer -a is a primitive root (mod m). 2. The integer a + b is not a primitive root (mod m). If b ≡ ak (mod m), then (m, k) = 1.

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter2: The Integers

Section2.5: Congruence Of Integers

Problem 32E: 32. Prove that if is an integer, then either or . (Hint: Consider the cases where is even and...

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Question

Prove or give a counterexample:

1. The integer -a is a primitive root (mod m).

2. The integer a + b is not a primitive root (mod m).

If b ≡ a^k (mod m), then (m, k) = 1.

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