Congruence with rational numbers

Let $r^2-ms^2 \in \mathbb {Z}$, and suppose that m is a square free integer with r,s not integers, prove that $m \equiv 1 \ (mod \ 4)$

Proof so far.

I have $r^2-ms^2 = n \ \ \ \ \ n \in \mathbb {Z}$
$m = \frac {r^2-n}{s^2}$