Simple proof involving integers

Question

Does this look ok to you?

let $m, n$ be any integers and $mn$ and $m + n$ are both even, prove that $m$ and $n$ are both even.

So $mn$ and $m+n$ are integers from what we are given we can assume even integers.

$mn+m+n=2(j+p)$ for some $j$ and $p$ in the integers

$(m+1)(n+1)=2(j+p)+1$

so $(m+1)(n+1)$ is odd it follows $m+1$ and $n+1$ are odd and so $n$ and $m$ are even.

Thanks a lot guys

Answer 1

Yes your proof is correct.

What I really like about it is avoiding different cases for $m$ and $n$

You proved your statement in one shot and that deserves merit.