Prove that ifpis a prime number andpdoes not equal 3, then 3 divides $\displaystyle p^2 + 2$. I'm given a hint that says, "Whenpis divided by 3, the remainder is either 0, 1, or 2. That is, for some integer k, p=3k or p=3k+1 or p=3k+2. I understand the hint and the initial statement, I just don't know where to start.