Prove that if $n^2$ is even then $n$ is even Assume that $n^2$ is even
Therefore $n^2 = 2k$ for some integer $k$.
How do I finish this proof?

I think it's best to use a proof by cases here.  .
Case 1:  $n$ is even.  Both $n^2$ and $n$ are even, so the statement "if n^2 is even then n is even" holds.  
Case 2:  $n$ is odd.  $n^2$ is odd, so the statement "if n^2 is even then n is even" is inconsequential and still holds.
