8. Find all solutions in positive integers of the diophantine equation $x^{2}+2 y^{2}=z^{2}$.
8. $x=\frac{1}{2}\left(m^{2}-2 n^{2}\right), y=m n, z=\frac{1}{2}\left(m^{2}+2 n^{2}\right)$ where $m$ and $n$ are positive integers, $x=\frac{1}{2}\left(2 m^{2}-n^{2}\right), y=m n, z=\frac{1}{2}\left(2 m^{2}+n^{2}\right)$ where $m$ and $n$ are positive integers, $m>n / \sqrt{2}$, and $n$ is even