{"schema":"vela.problem-packet.v0.1","problem":537,"statement":"Let $\\epsilon>0$ and $N$ be sufficiently large. If $A\\subseteq \\{1,\\ldots,N\\}$ has $\\lvert A\\rvert \\geq \\epsilon N$ then must there exist $a_1,a_2,a_3\\in A$ and distinct primes $p_1,p_2,p_3$ such that\\[a_1p_1=a_2p_2=a_3p_3?\\]","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)"}