Erdős problem 686

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 $m≥n+k$ ?

Sources

The source's own material, retained exactly.

8 retained statements36c6d0fef71a

FormalConjectures/ErdosProblems/

686.lean

Retained formal statement8 of 8

Can $25$ be written as $25=\frac{\prod_{1\leq i\leq k}(m+i)}{\prod_{1\leq i\leq k}(n+i)}$ for some $k≥2$ and $m≥n+k$ ?

FormalConjectures/ErdosProblems/686.leanErdos686.erdos_686.variants.twenty_five1 lineExact file

1sorry ↔ ∃ k ≥ 2, ∃ n, ∃ m ≥ n + k, 25 = ↑(∏ i ∈ Finset.Icc 1 k, (m + i)) / ↑(∏ i ∈ Finset.Icc 1 k, (n + i))

OpenStatement only, no proof