A pair of positive integers $\displaystyle (x, y)$ is called 'square' if both $\displaystyle x + y $and $\displaystyle xy$ are perfect square numbers. E.g. $\displaystyle (5, 20)$ is 'square' since $\displaystyle 5 + 20 = 25$ and $\displaystyle 5 x 20 = 100$, both which are perfect squares.

Prove no square pair exists in which one of its numbers is 3.

I'm not sure how to do this, but I think it involves mods in the solution.

Please help, thanks, BG