Prove that if $n^2 -2n +2$ is odd then $n$ is odd 
Prove that if $n^2 -2n +2$ is odd then $n$ is odd

I was wondering if you would prove this by using proof by contrapostive. I tried using proof by contrapostive, but I end up with the wrong answer.

$$n^2-2n+2=(n-3)(n+1)+5$$ will be odd $$(n-3)(n+1)$$ is even
iff $n-3$  is even as $n+1,n-3$  have same parity
Alternatively, 
$n^2-2n+2=(n-1)^2+1$ will be odd iff $(n-1)^2$ is even
$\iff n-1$ is even
