Answered: Prove that for p ≥ 3 a prime, there is…

Prove that for p ≥ 3 a prime, there is only one integer among {1, 2, . . . , p} of order 2 modulo p, and this integer is p − 1.

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter2: The Integers

Section2.4: Prime Factors And Greatest Common Divisor

Problem 5E: Prove that if p and q are distinct primes, then there exist integers m and n such that pm+qn=1.

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Prove that for p ≥ 3 a prime, there is only one integer among {1, 2, . . . , p}
of order 2 modulo p, and this integer is p − 1.

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