{"schema":"vela.problem-packet.v0.1","problem":894,"statement":"Let $A=\\{n_1<n_2<\\cdots\\}\\subset \\mathbb{N}$ be a lacunary sequence (so there exists some $\\epsilon>0$ with $n_{k+1}\\geq (1+\\epsilon)n_k$ for all $k$). Is it true that there must exist a finite colouring of $\\mathbb{N}$ with no monochromatic solutions to $a-b\\in A$?","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)"}