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Math Help - Sums of powers in integers

  1. #1
    Senior Member I-Think's Avatar
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    Apr 2009
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    288

    Sums of powers in integers

    Show that there are no integral solutions to the equation
    x^4+131=3y^4

    Need some helpful hints please

    I've been considering this equation mod 131, so
    x^4=3y^4 (mod 131)
    and then I would demonstrate this is impossible.

    But I cannot seem to do so, any hints please?
    And thank you
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  2. #2
    Senior Member roninpro's Avatar
    Joined
    Nov 2009
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    Try looking at the equation modulo 5. There won't be any solutions.
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