{"schema":"vela.problem-packet.v0.1","problem":483,"statement":"Let $f(k)$ be the minimal $N$ such that if $\\{1,\\ldots,N\\}$ is $k$-coloured then there is a monochromatic solution to $a+b=c$. Estimate $f(k)$. In particular, is it true that $f(k) < c^k$ for some constant $c>0$?","status":"open","seam":"raw","closureRoutes":[],"obligations":[],"attestations":[],"attempts":[],"velaLean":[],"oeis":[{"id":"A030126","name":"Schur's numbers (version 1).","terms":"2,5,14,45,161","url":"https://oeis.org/A030126"}],"generated_note":"derived view; the signed event log is the source of truth (vela check / vela reproduce)"}