{"schema":"vela.problem-packet.v0.1","problem":1202,"statement":"Let $\\epsilon,\\eta>0$. Does there exist a $k$ such that, given any set of $k$ primes $p_1<\\cdots<p_k<n^{1-\\epsilon}$, each with a set $A_i$ of $\\frac{p_i-1}{2}$ many congruence classes modulo $p_i$, the number of $m\\leq n$ such that $m\\not\\in A_i\\pmod{p_i}$ for all $i$ is at most $\\epsilon n$?","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)"}