I'm trying to go through the MIT opencourseware Mathematics for Computer Science (6.042J). I've been stumped for half a day trying to figure it out. Something isn't clicking, and I could use some help.
Here is the problem:
Suppose that $w^2 + x^2 + y^2 = z^2$, where $w$, $x$, $y$, and $z$ always denote positive integers.
(Hint: It may be helpful to represent even integers as $2i$ and odd integers as $2j + 1$, where $i$ and $j$ are integers)
Prove the proposition: $z$ is even if and only if $w$, $x$, and $y$ are even. Do this by considering all the cases of $w$, $x$, $y$ being odd or even.