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Math Help - Algebraic GCD problem

  1. #1
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    Algebraic GCD problem

    Prove that for every n, (n+1,n^2-n+1) is 1 or 3.
    Last edited by Deepu; January 21st 2010 at 04:41 PM.
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  2. #2
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    Dear Deepu,

    (n+1,n^2-n+1)=d

     d\mid{n+1} \mbox{ and }d\mid{n^2-n+1}

    d\mid{(n+1)^2-3n}

    d\mid{3n}

    d\mid{n+1}\Rightarrow d\mid{(3n+3)}

     d\mid{3}

     d=1 \mbox{ or }d=3

    Hope this helps.
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  3. #3
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    how does d|3n?
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  4. #4
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    Dear Deepu,

    d\mid{(n+1)^2-3n}\mbox{ and }d\mid{(n+1)}

    d\mid{3n}

    Hope this helps.
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