{"schema":"vela.problem-packet.v0.1","problem":53,"statement":"Let $A$ be a finite set of integers. Is it true that, for every $k$, if $\\lvert A\\rvert$ is sufficiently large depending on $k$, then there are least $\\lvert A\\rvert^k$ many integers which are either the sum or product of distinct elements of $A$?","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)"}