{"schema":"vela.problem-packet.v0.1","problem":484,"statement":"Prove that there exists an absolute constant $c>0$ such that, whenever $\\{1,\\ldots,N\\}$ is $k$-coloured (and $N$ is large enough depending on $k$) then there are at least $cN$ many integers in $\\{1,\\ldots,N\\}$ which are representable as a monochromatic sum (that is, $a+b$ where $a,b\\in \\{1,\\ldots,N\\}$ are in the same colour class and $a\\neq b$).","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)"}