Prove the given statements

(c) For every integer n, the number 3(n 2 + 2n + 3) 2n 2 is a perfect square.

(d) If n = 25, 100, or 169, then n is a perfect square and is a sum of perfect squares.

(e) The square of an odd integer equals 8k + 1 for some integer k.

(f) Sum of squares of two odd integers cannot be a perfect squar e.