{"schema":"vela.problem-packet.v0.1","problem":635,"statement":"Let $t\\geq 1$ and $A\\subseteq \\{1,\\ldots,N\\}$ be such that whenever $a,b\\in A$ with $b-a\\geq t$ we have $b-a\\nmid b$. How large can $\\lvert A\\rvert$ be? Is it true that\\[\\lvert A\\rvert \\leq \\left(\\frac{1}{2}+o_t(1)\\right)N?\\]","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)"}