Solution of Erdős problem $\mathrm{\#}443$

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