Symmetrically paired equation

Obviously, none of $x,y$ can be equal to zero. If one of $x,y$ is positive and the other is negative, then the LHS is negative (no solution). Both $x,y$ should be either positive or negative, which automatically impose limits on the absolute values of them ( $min(|x|,|y|) \leq 2$ ). The rest is just trying a couple of integers in the mentioned ranged considering symmetry of the equation, wrt $x$ and $y$ . The pairs are $(1,2)$ , $(2,1)$ , $(-1,-20)$ ,and $(-20,-1)$