Let $S(n)$ denote the largest integer such that, for all $1 ≤ k < n$, the binomial coefficient
$\binom{n}{k}$ is divisible by $p^S(n)$ for some prime $p$ (depending on $k$).Then
$\limsup S(n) = \infty$.
See solution in the comments on erdosproblems.com, and
https://github.com/teorth/analysis/blob/3522239c96742eaa0b3e8db9e7d41fe4c4907b37/analysis/Analysis/Misc/erdos_379.lean#L111
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