$x^2+y^2=2z^2$, positive integer solutions Determine all positive integer solutions of the equation $x^2+y^2=2z^2$.
First I assume $x \geq y$, and I have $x^2-z^2=z^2-y^2$. Then I have $(x-z)(x+z)=(z-y)(z+y)$, but from here, I don't know how it can help me to describe solutions (I know that there are infinitely many). 

Just a start:
Note that $$\left(\frac{x-y}{2}\right)^2 + \left(\frac{x+y}{2}\right)^2=\frac{x^2+y^2}{2}=z^2.$$
And $\frac{x-y}{2}$ and $\frac{x+y}{2}$ are integers (why?)
So you need to find solutions to $u^2+v^2=z^2$.
