{"schema":"vela.problem-packet.v0.1","problem":387,"statement":"Is there an absolute constant $c>0$ such that, for all $1\\leq k< n$, the binomial coefficient $\\binom{n}{k}$ has a divisor in $(cn,n]$?","status":"open","seam":"raw","closureRoutes":[],"obligations":[],"attestations":[],"attempts":[{"id":"att_db3585892bb3e4de","kind":"partial_proof","claim":"Erdős 387 (Schinzel) is OPEN; this is not a settlement. Rigorous contribution: a clean reduction. PROVEN (Legendre/Kummer): for 1≤k≤n/2 every prime in (n−k,n] divides C(n,k), so whenever that window contain","grade":"partial_proof","gateStatus":"needs_verification","superseded":false}],"velaLean":[],"oeis":[],"generated_note":"derived view; the signed event log is the source of truth (vela check / vela reproduce)"}