Question: (a) Fermat's Theorem. If p is a prime, prove that ap a (mod p) for each a Z. [How is this related to

(a) Fermat's Theorem. If p is a prime, prove that ap ≡ a (mod p) for each a ∈ Z. [How is this related to Exercise 22(a) of Section 14.3?]
(b) Euler's Theorem. For each n ∈ Z+, n > 1, and each a ∈ Z, prove that if gcd(a, n) = 1, then a

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a In Z p there are p 1 elements so by Exercise 8 for each x Z p x p1 1 or x p1 1 mod p ... View full answer

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