The question is:
r divides xy and s divides xy but gcd(r,s) = 1. Show that r divides xy/s
I am having a hard time finding a starting point for this problem. I believe I could use
xr + ys = 1 since gcd(r,s) = 1. I also know that since r|xy then there is an integer n such that xy = rn and since s|xy then there is an integer m such that xy = sm. Are these facts enough to do this proof or is there something that I am unaware of? I'm not looking for the answer to the problem as much as I am looking to be nudged in the right direction.