erdos_389

Is it true that for every $n \geq 1$ there is a $k$ such that $$ n(n + 1) \cdots (n + k - 1) \mid (n + k) \cdots (n + 2k - 1)? $$

theorem erdos_389 : answer(sorry) ↔
    ∀ n ≥ 1, ∃ k ≥ 1, ∏ i ∈ Finset.range k, (n + i) ∣ ∏ i ∈ Finset.range k, (n + k + i)

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