{"schema":"vela.problem-packet.v0.1","problem":1114,"statement":"Let $f(x)\\in \\mathbb{R}[x]$ be a polynomial of degree $n$ whose roots $\\{a_0<\\cdots<a_n\\}$ are all real and form an arithmetic progression. The differences between consecutive zeros of $f'(x)$, beginning from the midpoint of $(a_0,a_m)$ towards the endpoints, are monotonically increasing.","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)"}