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Thread: Proof help

  1. #1
    Mar 2009

    Proof help

    Prove that if u is an odd integer, then the equation x^2 + x - u=0 has no solution that is an integer.

    You can do this one of two ways, proof by contra positive, or proof by contradiction. I am a little confused on how I want to approach this.

    If anyone has any insight, I would be more than appreciative. Thanks in advance.
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  2. #2
    MHF Contributor red_dog's Avatar
    Jun 2007
    Medgidia, Romania
    If x is even then $\displaystyle x^2+x-u$ is odd.

    If x is odd then $\displaystyle x^2+x-u$ is also odd.

    So it can't be zero.
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