{"schema":"vela.problem-packet.v0.1","problem":379,"statement":"Let $S(n)$ denote the largest integer such that, for all $1\\leq k<n$, the binomial coefficient $\\binom{n}{k}$ is divisible by $p^{S(n)}$ for some prime $p$ (depending on $k$). Is it true that\\[\\limsup S(n)=\\infty?\\]","status":"solved","seam":"raw","closureRoutes":[],"obligations":[],"attestations":[],"attempts":[],"velaLean":[],"oeis":[],"generated_note":"derived view; the signed event log is the source of truth (vela check / vela reproduce)"}