So, I think that you mean that
n²+m² is even? (the "plus" sign is missing, but I think this is correct).
this can only happen if either:
both n and m are even
or
both n and m are odd
That's because a sum of two expressions is even if either both or none of the expressions summed is even, and a power of a number is even only if the number is even too.
are those some of the options?
yes!
n and m are even,- possible!
n and m are odd, -possible!
n+m is even, - possible; it would be the case if either both n and m are even or both n and m are odd n+m is odd,
so the option we'll choose is:
none of these are impossible