.

.

is fixed odd integer.

and .

Find all possible values of .

I know that is odd and is even. I know

I can find that (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 , 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 and (I don't have time to try it now, so I can't give feedback).