{"schema":"vela.problem-packet.v0.1","problem":1185,"statement":"Let $\\delta>0$ and $k\\geq 3$. Is it true that there exists $m\\geq 1$ (depending only on $\\delta$ and $k$) such that, for all large $N$, if $A,B\\subseteq \\{1,\\ldots,N\\}$ with $\\lvert A\\rvert \\geq \\delta N$ and $\\lvert B\\rvert \\geq m$ then there is a non-trivial $k$-term arithmetic progression in $A$ whose common difference is in $B-B$?","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)"}