Let q 2 be such that , q|ab q|a or q|b. Show that is irrational.

The hint of the book said to imitate the proof that is irrational. I did it by letting and assuming is rational. So 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.