Differences of Two Squares

Let $M = \{t : t = m^2 - n^2,\ m, n \in \mathbb{Z}\}$.

1. Prove that the product of any two elements of $M$ is in $M$. 2. Are $32, 33, 34$ in $M$? Why? 3. Give (with proof) a necessary and sufficient condition for an even number $2k$ to belong to $M$.