{"schema":"vela.problem-packet.v0.1","problem":280,"statement":"Let $n_1<n_2<\\cdots $ be an infinite sequence of integers with associated $a_k\\pmod{n_k}$, such that for some $\\epsilon>0$ we have $n_k&#62;(1+\\epsilon)k\\log k$ for all $k$. Then\\[\\#\\{ m&#60;n_k : m\\not\\equiv a_i\\pmod{n_i} \\textrm{ for }1\\leq i\\leq k\\}\\neq o(k).\\]","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)"}