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Thread: GCD Proof

  1. April 26th 2012, 05:36 PM #1
    jmedsy
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    GCD Proof

    I have a hunch that this problem is solved using using the theorem (a +cb, b) = (a, b) where a, b, and c are all integers (a and b are not both zero).

    Show that if n is a positive integer, then (n^2 + 2, n^3 +1) = 1, 3, or 9.

    I just can't get this to work out.
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  2. April 26th 2012, 11:56 PM #2
    ignite
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    Re: GCD Proof

    (n^2+2,n^3+1)=(n(n^2+2),n^3+1)=(n^2+2,2n-1)
    =(n^2+2,n(2n-1))=(2n-1,n+4)=(n+4,9)=1,3,9
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