Erdős problem 727 · problems.science

Let $k ≥ 2$ . Does $((n+k)!)^2∣(2n)!$ hold for infinitely many $n$ ?

Sources

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

4 retained statements2415f78e850a

FormalConjectures/ErdosProblems/

727.lean

Retained formal statement3 of 4

Erdős, Graham, Ruzsa, and Straus observe that the method of Balakran can be further used to prove that there are infinitely many $n$ such that $(n+k)!(n+1)!∣(2n)!$

FormalConjectures/ErdosProblems/727.leanErdos727.erdos_727.variants.k_1_21 lineExact file

1∀ (k : ℕ), 2 ≤ k → {n | (n + k).factorial * (n + 1).factorial ∣ (2 * n).factorial}.Infinite

SolvedStatement only, no proof

Sources

Search problems.science