{"schema":"vela.problem-packet.v0.1","problem":138,"statement":"Let the van der Waerden number $W(k)$ be such that whenever $N\\geq W(k)$ and $\\{1,\\ldots,N\\}$ is $2$-coloured there must exist a monochromatic $k$-term arithmetic progression. Improve the bounds for $W(k)$ - for example, prove that $W(k)^{1/k}\\to \\infty$.","status":"open","seam":"raw","closureRoutes":[],"obligations":[],"attestations":[{"verdict":"variant","attestedBy":"reviewer:will-blair","formalRef":"erdos_138.variants.difference.lean","targetFinding":"vf_20dd984366cd93dd"}],"attempts":[],"velaLean":[],"oeis":[{"id":"A005346","name":"Van der Waerden numbers W(2,n).","terms":"1,3,9,35,178,1132","url":"https://oeis.org/A005346"}],"generated_note":"derived view; the signed event log is the source of truth (vela check / vela reproduce)"}