{"schema":"vela.problem-packet.v0.1","problem":275,"statement":"If a finite system of $r$ congruences $\\{ a_i\\pmod{n_i} : 1\\leq i\\leq r\\}$ (the $n_i$ are not necessarily distinct) covers $2^r$ consecutive integers then it covers all integers.","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)"}