{"schema":"vela.problem-packet.v0.1","problem":688,"statement":"Define $\\epsilon_n$ to be maximal such that there exists some choice of congruence class $a_p$ for all primes $n^{\\epsilon_n}<p\\leq n$ such that every integer in $[1,n]$ satisfies at least one of the congruences $\\equiv a_p\\pmod{p}$.Estimate $\\epsilon_n$ - in particular is it true that $\\epsilon_n=o(1)$?","status":"open","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)"}