2. Let n ∈ N and x, y ∈ Z. Prove:

(a) (x + y) mod n = (x mod n) + (y mod n) mod n;

(b) (xy) mod n = (x mod n) (y mod n) mod n; and

(c) x^t mod n = (x mod n)^t mod n for all t∈ N.