{"schema":"vela.problem-packet.v0.1","problem":1198,"statement":"If $\\mathbb{N}$ is $2$-coloured then must there exist an infinite set $A=\\{a_1<\\cdots\\}$ such that all expressions of the shape\\[\\prod_{i\\in S_1}a_i+\\cdots+\\prod_{i\\in S_k}a_i,\\]for disjoint $S_1,\\ldots,S_k$ (excluding the trivial expressions $a_i$) are the same colour?","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)"}