{"schema":"vela.problem-packet.v0.1","problem":140,"statement":"Let $r_3(N)$ be the size of the largest subset of $\\{1,\\ldots,N\\}$ which does not contain a non-trivial $3$-term arithmetic progression. Prove that $r_3(N)\\ll N/(\\log N)^C$ for every $C>0$.","status":"solved","seam":"raw","closureRoutes":[],"obligations":[],"attestations":[],"attempts":[],"velaLean":[],"oeis":[{"id":"A003002","name":"Size of the largest subset of the numbers [1...n] which does not contain a 3-term arithmetic progression.","terms":"0,1,2,2,3,4,4,4,4,5,5,6,6,7,8,8,8,8,8,8,9,9,9,9,10,10,11,11,11,11,12,12,13,13,13,13,14,14,14,14,15,16,16,16,16,16,16,16,","url":"https://oeis.org/A003002"}],"generated_note":"derived view; the signed event log is the source of truth (vela check / vela reproduce)"}