OPEN
For integer $n\geq 1$ we define the factor difference set of $n$ by
\[D(n) = \{\lvert a-b\rvert : n=ab\}.\]
Is it true that, for every $k\geq 1$, there exist integers $N_1<\cdots<N_k$ such that
\[\lvert \cap_i D(N_i)\rvert \geq k?\]
A question of Erdős and Rosenfeld
[ErRo97], who proved this is true for $k=2$. Jiménez-Urroz
[Ji99] proved this for $k=3$ and Bremner
[Br19] proved this for $k=4$.
