{"schema":"vela.problem-packet.v0.1","problem":27,"statement":"An $\\epsilon$-almost covering system is a set of congruences $a_i\\pmod{n_i}$ for distinct moduli $n_1<\\ldots<n_k$ such that the density of those integers which satisfy none of them is $\\leq \\epsilon$. Is there a constant $C>1$ such that for every $\\epsilon&#62;0$ and $N\\geq 1$ there is an $\\epsilon$-almost covering system with $N\\leq n_1&#60;\\cdots &#60;n_k\\leq CN$?","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)"}