Prove that for every integer $x$, if $x^2 - 2x + 7$ is even, then $x$ is odd.
Assume x is even, we will prove $x^2-2x+7$ is odd.
Then there exists some integer k where $x=2k$
Then $(2k)^2 - 2(2k) + 7 = 4k^2 - 4k + 7 = 2(2k^2 - 2k) + 7$
I'm not sure if I'm doing this properly, I thought that I should get 2K + 1, but I'm getting 2k+7?