Question 95
Let $A$ and $B$ be sets of positive integers with $|A| \ge 2$ and $|B| \ge 2$. Let $S$ be a set consisting of $|A| + |B| - 1$ numbers of the form $ab$ where $a \in A$ and $b \in B$. Prove that there exist pairwise distinct $x, y, z \in S$ such that $x$ is a divisor of $yz$.