{"schema":"vela.problem-packet.v0.1","problem":519,"statement":"Let $z_1,\\ldots,z_n\\in \\mathbb{C}$ with $z_1=1$. Must there exist an absolute constant $c>0$ such that\\[\\max_{1\\leq k\\leq n}\\left\\lvert \\sum_{i}z_i^k\\right\\rvert>c?\\]","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)"}