Erdős Problem #885 — 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…

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 $\lvert \cap_i D(N_i)\rvert \geq k?$