And since and have no common factors, q must divide so, by your condition, q must divide m. m= qp for some integer p and so and then , . Since , and thus p, is a factor of and so not a factor of , we must have q a factor of , again, by your condition on q, a factor of n, contradicting the fact that m and n have no common factors.and then . Thus, .
From here, I must consider if m is even or odd. If m is odd, it must follow that both q and is odd.
It does not seem I could reach any contradiction from the assumption , q|ab q|a or q|b.
Please help, thanks a lot.[/QUOTE]