{"schema":"vela.problem-packet.v0.1","problem":495,"statement":"Let $\\alpha,\\beta \\in \\mathbb{R}$. Is it true that\\[\\liminf_{n\\to \\infty} n \\| n\\alpha \\| \\| n\\beta\\| =0\\]where $\\|x\\|$ is the distance from $x$ to the nearest integer?","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)"}