The question I am working on is:
Prove that if $m+n$ and $n+p$ are even integers, where $m$, $n$,and $p$ are integers, then $m+p$ is even. What kind of proof did you use?
I was thinking--and I aware that this may not be the most efficient method--of proving four different cases: $m$ and $p$ are both even; $m$ and $p$ are both odd; or $m$ and $p$ are opposite parity. Would this work? Or is there a better way?