{"schema":"vela.problem-packet.v0.1","problem":818,"statement":"Let $A$ be a finite set of integers such that $\\lvert A+A\\rvert \\ll \\lvert A\\rvert$. Is it true that\\[\\lvert AA\\rvert \\gg \\frac{\\lvert A\\rvert^2}{(\\log \\lvert A\\rvert)^C}\\]for some constant $C>0$?","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)"}