Prove the following statements using either direct or contrapositive proof: a. Suppose x, and y are integers. If x + y is even, then x and y have the same parity. b. If a is an integer and a = 1(mod5), then a^2 = 1(mod5). c. If n = (2^k) - 1 for a natural number k, then every entry in Row n of Pascal’s Triangle is odd. d. If a = b(mod n), then gcd(a,n) = gcd(b,n).