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Math Help - Proof by Cases

  1. #1
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    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.
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  2. #2
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    Quote Originally Posted by nick898 View Post
    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.
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