Let p be a prime, a ∈ Z. Prove that ap − a is divisible by p.

Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter6: More On Rings
Section6.1: Ideals And Quotient Rings
Problem 19E: 19. Let and be nonzero integers. Prove that if and only if divides .
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Let p be a prime, a ∈ Z. Prove that ap − a is divisible by p.

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