proofs involving congruence of integers Let n, m be integers. Prove that if n ≡ 1( mod 2) and m ≡ 3( mod 4), then n^2 +m ≡ 0(mod4)
My thought process is  that n=3 and m=7 so n^2 would be 9+7 but then i do not believe that would equal 0(mod4) which i think would equal 4. 
Any direction would help on where to start or how to attack this problem.

Hint:  Consider two cases:
$n\equiv 1\text{mod}4$
or 
$n\equiv 3\text{mod}4$
What can you say about $n^2\text{mod}4$ in either of those cases?
