Integer solutions of an algebraic equation I'm trying to find integer solutions $(a,b,c)$ of the following algebraic equation with additional conditions $b>a>0$, $c>0$.
$(-a^2+b^2+c^2)(a^2-b^2+c^2)(a^2+b^2-c^2) + 2 a b (-a^2+b^2+c^2)(a^2-b^2+c^2) - 2 b c (a^2-b^2+c^2)(a^2+b^2-c^2) - 2 a c (-a^2+b^2+c^2) (a^2+b^2-c^2) = 0$
Is it possible to do using some math packages?

The equation is homogeneous in 3 variables, thus it is associated with a plane curve. First, I would check if the curve has genus less than 2. If the genus is 0 or 1, the curve is parametrizable or elliptic, respectively. In particular, for parametrizable curves, you can generate integer solutions, provided that at least one integer solution exists and you know it.
