{"schema":"vela.problem-packet.v0.1","problem":310,"statement":"Let $\\alpha >0$ and $N\\geq 1$. Is it true that for any $A\\subseteq \\{1,\\ldots,N\\}$ with $\\lvert A\\rvert \\geq \\alpha N$ there exists some $S\\subseteq A$ such that\\[\\frac{a}{b}=\\sum_{n\\in S}\\frac{1}{n}\\]with $a\\leq b =O_\\alpha(1)$?","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)"}