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 $m≥n+k$ ?

Sources

Browse retained paths and inspect the exact material available for this Problem.

8 retained statements2415f78e850a

FormalConjectures/ErdosProblems/

686.lean

Retained formal statement3 of 8

The number $4$ cannot be written as $4=\frac{\prod_{1\leq i\leq 3}(m+i)}{\prod_{1\leq i\leq 3}(n+i)}$ for $m≥n+3$ !

See [comment section on erdosproblems.com](https://www.erdosproblems.com/forum/thread/686#post-4599)

FormalConjectures/ErdosProblems/686.leanErdos686.erdos_686.variants.four_three1 lineExact file

1¬∃ n, ∃ m ≥ n + 3, 4 = ↑(∏ i ∈ Finset.Icc 1 3, (m + i)) / ↑(∏ i ∈ Finset.Icc 1 3, (n + i))

SolvedStatement only, no proof