{"schema":"vela.problem-packet.v0.1","problem":190,"statement":"Let $H(k)$ be the smallest $N$ such that in any finite colouring of $\\{1,\\ldots,N\\}$ (into any number of colours) there is always either a monochromatic $k$-term arithmetic progression or a rainbow arithmetic progression (i.e. all elements are different colours). Estimate $H(k)$. Is it true that\\[H(k)^{1/k}/k \\to \\infty\\]as $k\\to\\infty$?","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)"}