For any integer, k, k^2 + 2k + 3 is even if and only if 4 divides k^2 -2k-7. (Note: You may use a fact, we may not yet have proven in class, namely, if 2 divides n^2 for some integer n, then 4 divides n^2. Simply cite this as, "a fact about squares of integers that are even.")