Solution of Erdős problem $\# 443$

Stijn Cambie

Solution of Erdős problem $\# 443$

Combinatorics 2026-07-28 v1 Number Theory

Authors: Stijn Cambie

Abstract

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

Cite

@article{arxiv.2607.25928,
  title  = {Solution of Erdős problem $\# 443$},
  author = {Stijn Cambie},
  journal= {arXiv preprint arXiv:2607.25928},
  year   = {2026}
}

Comments

1 Page (filler in American Mathematical Monthly)