Q:

Let $n$ be an integer. Then $n^2 + 7$ is odd only if $n$ is even.

I want to prove this proposition but unsure how to start it.
I started off with:  

Assume $n$ is even, then $n^2$ is even.
  When $even + odd = odd$.
  Thus, $n^2 + 7$ is odd only if $n$ is even.

Does this make sense for a proof? If not how could I improve it?

A:

$n^2 + 7$ is odd $\Leftrightarrow$ $n^2$ is even $\Leftrightarrow$ $n$ is even

