Erdős problem 686 · problems.science

Can every integer $N≥2$ be written as $N=\frac{\prod_{1\leq i\leq k}(m+i)}{\prod_{1\leq i\leq k}(n+i)}$ for some $k≥2$ and $m≥n+k$ ?

No current result

No reviewed Result is current in Vela Mathematics Program. Retained source material is shown below.

FormalConjectures/ErdosProblems/686.lean

Formal Conjectures

FormalConjectures/ErdosProblems/686.leanErdos686.erdos_6861 lineExact file

1sorry ↔ ∀ N ≥ 2, ∃ k ≥ 2, ∃ n, ∃ m ≥ n + k, ↑N = ↑(∏ i ∈ Finset.Icc 1 k, (m + i)) / ↑(∏ i ∈ Finset.Icc 1 k, (n + i))

OpenStatement only, no proof

Work these sources record against this Problem. Source-reported attribution, not reviewed here.