{"schema":"vela.problem-packet.v0.1","problem":974,"statement":"Let $z_1,\\ldots,z_n\\in \\mathbb{C}$ be a sequence such that $z_1=1$. Suppose that the sequence of\\[s_k=\\sum_{1\\leq i\\leq n}z_i^k\\]contains infinitely many $(n-1)$-tuples of consecutive values of $s_k$ which are all $0$. Then (essentially)\\[z_j=e(j/n),\\]where $e(x)=e^{2\\pi ix}$.","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)"}