{"schema":"vela.problem-packet.v0.1","problem":496,"statement":"Let $\\alpha \\in \\mathbb{R}$ be irrational and $\\epsilon>0$. Are there positive integers $x,y,z$ such that\\[\\lvert x^2+y^2-z^2\\alpha\\rvert <\\epsilon?\\]","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)"}