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Math Help - 2p^2 - q^2 and 2q^2 - p^2 as perfect squares simultaneously

  1. #1
    Junior Member
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    Omagh
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    2p^2 - q^2 and 2q^2 - p^2 as perfect squares simultaneously

    If I can show that

    2p^2-q^2 and 2q^2-p^2

    can only be perfect squares simultaneously when

    p\ =\ m^2+n^2\ =\ u^2-2uv-v^2

    and

    q\ =\ m^2-2mn-n^2\ =\ u^2+v^2

    is this enough to say that p = q ?

    [edit]

    Forgot to say that p and q are integers > 0

    Thanks
    Last edited by procyon; October 3rd 2011 at 10:29 AM.
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