{"schema":"vela.problem-packet.v0.1","problem":467,"statement":"Prove the following for all large $x$: there is a choice of congruence classes $a_p$ for all primes $p\\leq x$ and a decomposition $\\{p\\leq x\\}=A\\sqcup B$ into two non-empty sets such that, for all $n<x$, there exist some $p\\in A$ and $q\\in B$ such that $n\\equiv a_p\\pmod{p}$ and $n\\equiv a_q\\pmod{q}$.","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)"}