Erdős problem 389

Is it true that for every $n \geq 1$ there is a $k$ such that $n(n + 1) \cdots (n + k - 1) \mid (n + k) \cdots (n + 2k - 1)?$

Sources

The source's own material, retained exactly.

2 retained statements36c6d0fef71a

FormalConjectures/ErdosProblems/

389.lean

Retained formal statement1 of 2

Is it true that for every $n \geq 1$ there is a $k$ such that $n(n + 1) \cdots (n + k - 1) \mid (n + k) \cdots (n + 2k - 1)?$

FormalConjectures/ErdosProblems/389.leanErdos389.erdos_3891 lineExact file

1True ↔ ∀ n ≥ 1, ∃ k ≥ 1, ∏ i ∈ Finset.range k, (n + i) ∣ ∏ i ∈ Finset.range k, (n + k + i)

OpenStatement only, no proof