First, note that if one of is then the other also must be If then is a divisor of
Assume and let where and
Rearrange the equation to get As the RHS is rational, the LHS would be irrational unless Hence
Finally, we have since
Hi,
I was hoping somebody could put me on the right line to prove this question. It says:
Let, be positive integers such that is a rational number. Prove that is a divisor of
I'm never very good at proofs as I never know where to start. Would one times by and see what happens (I have but I can't see anything helpful)?
Thanks very much in advance for any help!
First, note that if one of is then the other also must be If then is a divisor of
Assume and let where and
Rearrange the equation to get As the RHS is rational, the LHS would be irrational unless Hence
Finally, we have since