{"schema":"vela.problem-packet.v0.1","problem":143,"statement":"Let $A\\subset (1,\\infty)$ be a countably infinite set such that for all $x\\neq y\\in A$ and integers $k\\geq 1$ we have\\[ \\lvert kx -y\\rvert \\geq 1.\\]Does this imply that $A$ is sparse? In particular, does this imply that\\[\\sum_{x\\in A}\\frac{1}{x\\log x}<\\infty\\]or\\[\\sum_{\\substack{x <n\\\\ x\\in A}}\\frac{1}{x}=o(\\log n)?\\]","status":"open","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)"}