{"schema":"vela.problem-packet.v0.1","problem":1186,"statement":"Let $\\delta_k$ be such that in any $2$-colouring of $\\{1,\\ldots,n\\}$ there exist at least $(\\delta_k+o(1))n^2$ many monochromatic $k$-term arithmetic progressions. Give reasonable bounds (or even an asymptotic formula) for $\\delta_k$.","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)"}