{"schema":"vela.problem-packet.v0.1","problem":729,"statement":"Let $C>0$ be a constant. Are there infinitely many integers $a,b,n$ with $a+b> n+C\\log n$ such that the denominator of\\[\\frac{n!}{a!b!}\\]contains only primes $\\ll_C 1$?","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)"}