I have been having a little trouble with proofs, and would like to ask for a hint for this statement. I've already started it, however I'm unsure what I should be doing next.
Prove that if $n^2 + 10$ is odd then $n$ is odd.
My answer so far: Suppose that $n$ is an odd integer, and we want to prove $n^2 + 10$ is odd. There exists a $k$ that $n=2k+1$. By substituting for $n$, we get...
$(2k+1)^2 +10$ = $n^2 = 10$
$4k^2 + 4k + 11$ = $n^2 +10$
I am unsure what to do next.
EDIT: Thank you all for your hints and answers! They were all brilliant and my understanding for all kinds of proofs is a heck lot better! So much appreciated!