Let r, s, t, u be integers >= 1. Suppose r/s = t/u and both fractions are in lowest terms. Prove that r = t and s = u.
This problem seems like it should be obvious, but I cannot come up with a way to start it. I'm thinking that I might make use of gcd(r,s) = gcd(t,u) = 1, or by somehow showing that r & t and s & u have the same prime factorizations, but I'm not sure where to begin.