Prove that the equation $\displaystyle x^{2} + y^{2} = 7$ has no rational solutions.

I tried to go about this using the fact that for any integer $\displaystyle a$, $\displaystyle a^{2} \equiv 0(mod 4)$ or $\displaystyle a^{2} \equiv 1(mod4)$, but when I supposed that there existed a rational solution $\displaystyle (\frac{p}{q},\frac{m}{n})$ and arrived to the equation $\displaystyle (pn)^{2} + (qm)^{2} = 7(qn)^{2}$, I can't draw the conclusion I want. How do I go about this? Any help would be appreciated.