(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