What does the following mean: If $x^2 + y^2 = z^2$ some integers $z$, then $x$ and $y$ can't be both odd (otherwise, the sum of their squares would be $2$ modulo $4$, which can't be a square). So, one of them must be even?
I see that if $x$ and $y$ are both odd, then $z^2 = 4k+2 =2(2k+1)$. So $z^2$ is even. But why does it say above that... can't be square?