Lecture 5, problem 5.17

The answer should be yes, but the online answer says no.

The proof in the answer says to let p=m=n=2. The answer says that  2²| m·n ,which is basically 4|4. The answer also says that 4 doesn't divide 2, but the problem only says that either p divides m or p divides n. This means that 2 divides 2, so the answer doesn't work and the answer should be yes.