{"schema":"vela.problem-packet.v0.1","problem":728,"statement":"Let $C>0$ and $\\epsilon>0$ be sufficiently small. Are there infinitely many integers $a,b,n$ with $a\\geq \\epsilon n$ and $b\\geq \\epsilon n$ such that\\[a! b! \\mid n!(a+b-n)!\\]and $a+b>n+C\\log n$?","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)"}