{"schema":"vela.problem-packet.v0.1","problem":351,"statement":"Let $p(x)\\in \\mathbb{Q}[x]$ with positive leading coefficient. Is it true that\\[A=\\{ p(n)+1/n : n\\in \\mathbb{N}\\}\\]is strongly complete, in the sense that, for any finite set $B$,\\[\\left\\{\\sum_{n\\in X}n : X\\subseteq A\\backslash B\\textrm{ finite }\\right\\}\\]contains all sufficiently large 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)"}