{"schema":"vela.problem-packet.v0.1","problem":490,"statement":"Let $A,B\\subseteq \\{1,\\ldots,N\\}$ be such that all the products $ab$ with $a\\in A$ and $b\\in B$ are distinct. Is it true that\\[\\lvert A\\rvert \\lvert B\\rvert \\ll \\frac{N^2}{\\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)"}