Let $S (n)$ denote the largest integer such that, for all $1 \leq k < n$ , the binomial coefficient $(k n)$ is divisible by $p^{S (n)}$ for some prime $p$ (depending on $k$ ). Is it true that $lim sup S (n) = \infty ?$

Worked, still open.

number theory · solved · possible · formalized (Lean) · 0 attempts

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AMS 11 · solved (literature)

theorem erdos_379 : atTop.limsup (fun n => (S n : ℕ∞)) = ⊤

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