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Math Help - Proof about squares of odd numbers

  1. #1
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    Proof about squares of odd numbers

    Hello community. I've been having a hard time proving this: The sum of the squares of odd integers cannot be a perfect square. I'd appreciate any direct help or hint
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  2. #2
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    Re: Proof about squares of odd numbers

    Prove first that the sum of two odd squares is 2 more than a multiple of 4.

    This tells us that it is an even number, but not divisible by 4.

    But if this summed to a square, that square being even, would have to be a square of another even number, and thus 4 would divide it.
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    Re: Proof about squares of odd numbers

    Hehe was pretty straightforward. Thank you
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