{"schema":"vela.problem-packet.v0.1","problem":1147,"statement":"Let $\\alpha>0$ be an irrational number. Is the set\\[A=\\left\\{ n\\geq 1: \\| \\alpha n^2\\| < \\frac{1}{\\log n}\\right\\},\\]where $\\|\\cdot\\|$ denotes the distance to the nearest integer, an additive basis of order $2$?","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)"}