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Math Help - Diophantine equation

  1. #1
    MHF Contributor alexmahone's Avatar
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    Diophantine equation

    Find all integral solutions of the equation x^4+2x^3+2x^2+2x+5=y^2.

    My attempt:

    The equation can be re-written as

    (x^2+x+1)^2-x^2=y^2-2^2

    (x^2+2x+1)(x^2+1)=(y+2)(y-2)

    (x+1)^2(x^2+1)=(y+2)(y-2)

    By inspection (-1, 2), (-1, -2), (2, 7) and (2, -7) are solutions. Are these the only solutions?
    Last edited by CaptainBlack; July 24th 2011 at 02:28 AM. Reason: It is not our practice to delete threads
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