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Erdős problem 727

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

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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 nn such that (n+k)!(n+1)!∣(2n)!(n+k)!(n+1)!∣(2n)!

FormalConjectures/ErdosProblems/727.leanErdos727.erdos_727.variants.k_1_21 lineExact file
∀ (k : ℕ), 2 ≤ k → {n | (n + k).factorial * (n + 1).factorial ∣ (2 * n).factorial}.Infinite
SolvedStatement only, no proof