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Math Help - Find all possible values of a divisor

  1. #1
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    Find all possible values of a divisor

    m=6k+1.
     n=3k-1.
    k is fixed odd integer.
     a|m and a|n.
    Find all possible values of a.

    I know that m is odd and n is even. I know
     m=...,-17,-5,7,19,31,..
     n=...,-10,-4,2,8,14,20,...

    I can find that a=(6k+1)/q=(3k-1)/r (where q and r are any integers). I can even solve for k=[q(3k-1)-r]/[6r]. I guess I can say that when k is an integer in that format, then a divides m and n (or something along those lines). But that's all I've got.

    Frankly, I think the answer is a=\pm1, but cannot prove it.

    BTW, this is a take home quiz, so don't give answers. A hint of where to go would be nice, though.

    Edit: My friend suggests Euclidean Algorithm on the definition of m and n (I don't have time to try it now, so I can't give feedback).
    Last edited by MSUMathStdnt; September 15th 2011 at 05:08 PM.
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