# Math Help - Proof by Cases

1. ## Proof by Cases

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.

2. Originally Posted by nick898
Here is the problem:
Let a,b belong to the integers. If ab is odd, then a^2 + b^2 is even.
If $a \cdot b$ is odd then each of $a\;\&\;b$ is odd.
As well as each of $a^2\;\&\;b^2$ is odd.
The sum of two odds is even.
Look at $(a+b)^2$.