(a) Let p be a prime. Prove that if the integers a, b satisfy a ≡ b mod p then a^p ≡ b^p mod p^2. [Hint: Look at the proof of the Little Fermat Theorem.]
(b) Let Give an example of an even positive integer n and an integer a such that
a^n does not ≡ a mod n. By the Little Fermat Theorem we must have n > 2.