Prove: If n is odd and n|(a-b) and n|(a+b) then n|a and n|b
since n is odd, there is some number k such that
there are also integers p,q such that
$np=(a-b)$ and $nq = (a+b)$
(We want to show there are integers r,s such that)
I've only managed to make it this far into the proof, However, I've noted a few observations.
- p and q could be either odd or even
- a and b must be odd in order for their sum or difference to be divisible by n
Furthermore, my goal is to show that there are some integers r,s that are divisible by n.
I have attempted substitution, but it seems to be leading to dead ends.