For proofs, can we take for granted that an even number x an odd number is even? I'm supposed to prove that for ever natural number, n, n^2 + 2 is even. Proof: n^2 + n = n(n+1) Since n and n + 1 and two consecutive integers, one must be even and one must be odd so there product must be even. If something this basic is not required to prove, out of curiousity what would be the proof? And what is a good general rule of thumb for deciding what to prove or support in your proofs?