General integer solutions of the equation $a^{2} = (b+c)^{2}$?

Question

So I wonder if there is any know result about the general form of the integer solutions of $a^{2} = (b+c)^{2}$. A class of particular solutions is readily available, the class of all triples $(a,b,c)$ of integers such that exactly one of $b,c$ is $=0$ and $a=c$ or $a=b$ accordingly.

Answer 1

This really isn't the toughest class of Diophantine equation known. Of course $a^2=(b+c)^2$ iff $a=\pm(b+c)$, so we have parametric solutions $(a,b,c)=(t,u,t-u)$ and $(a,b,c)=(t,u,-t-u)$.