{"schema":"vela.problem-packet.v0.1","problem":998,"statement":"Let $\\alpha$ be an irrational number. Is it true that if, for all large $n$,\\[\\#\\{ 1\\leq m\\leq n : \\{ \\alpha m\\} \\in [u,v)\\} = n(v-u)+O(1)\\]then $u=\\{\\alpha k\\}$ and $v=\\{\\alpha \\ell\\}$ for some integers $k$ and $\\ell$?","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)"}