{"schema":"vela.problem-packet.v0.1","problem":281,"statement":"Let $n_1<n_2<\\cdots$ be an infinite sequence such that, for any choice of congruence classes $a_i\\pmod{n_i}$, the set of integers not satisfying any of the congruences $a_i\\pmod{n_i}$ has density $0$. Is it true that for every $\\epsilon>0$ there exists some $k$ such that, for every choice of congruence classes $a_i$, the density of integers not satisfying any of the congruences $a_i\\pmod{n_i}$ for $1\\leq i\\leq k$ is less than $\\epsilon$?","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)"}