Solution of Erdős problem $\#443$

Abstract

We prove that the size $\#\{k(m-k):1\le k\le m/2\}\cap \{l(n-l):1\le l\le n/2\}$ is $(mn{)}^{o(1)}$, but can be arbitrarily large. This resolves Erdős problem $\#443$.

1 Page (filler in American Mathematical Monthly)