{"schema":"vela.problem-packet.v0.1","problem":708,"statement":"Let $g(n)$ be minimal such that for any $A\\subseteq [2,\\infty)\\cap \\mathbb{N}$ with $\\lvert A\\rvert =n$ and any set $I$ of $\\max(A)$ consecutive integers there exists some $B\\subseteq I$ with $\\lvert B\\rvert=g(n)$ such that\\[\\prod_{a\\in A} a \\mid \\prod_{b\\in B}b.\\]Is it true that\\[g(n) \\leq (2+o(1))n?\\]Or perhaps even $g(n)\\leq 2n$?","status":"open","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)"}