{"schema":"vela.problem-packet.v0.1","problem":966,"statement":"Let $k,r\\geq 2$. Does there exist a set $A\\subseteq \\mathbb{N}$ that contains no non-trivial arithmetic progression of length $k+1$, yet in any $r$-colouring of $A$ there must exist a monochromatic non-trivial arithmetic progression of length $k$?","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)"}