We're in an integral domain with unity 1 $\neq$ 0. Suppose that the highest common factor between x,y is 1 and the highest common factor for x,z is 1.
Show that $x \mid yz$ implies that $x$ is a unit, or provide a counterexample.
I'm stuck. I don't have that we are in a unique factorization domain, I don't have that this ring is Noetherian.