Here is the problem:

Let a,b belong to the integers. If ab is odd, then a^2 + b^2 is even.

I can't seem to find a way to find a or b alone in this one. It seems like I might have to use a contrapositive proof here as well, but I can't see where that gets me. If I just use a direct proof then it seems harder to get a or b alone when their product is odd.