Currently learning about primitive Pythagorean triples and I'm having trouble approaching the following proof.
Given that $x, y, z$, is a primitive Pythagorean triple with $y$ even, I need to show:
$$x + y \equiv x - y \equiv 1,7 \pmod 8$$
So far all I've noticed is that $x+y$ and $x-y$ must be odd but I'm not sure how to determine the equivalence to each other $\bmod 8$. Could anyone give me a small push in the right direction?