# Math Help - Find all possible values of a divisor

1. ## 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).