1. Let n and m be positive integers, and consider the function : Z/nmZZ/nZ x Z/mZ given by ([a]nm)=([a]n, [a]m). (a) Prove that is well-defined independent of the integer a representing the equivalence class [a]nm by showing that: If a, b € Z such that [a]nm [b]nm in Z/nmZ, then ([an, am) = (bn. [b]m) as ordered pairs in Z/nZ x Z/mZ. Your proof should not mention the function p. (b) Prove that is a ring homomorphism. (c) If gcd (n, m) = 1, prove that is an isomorphism.