{"schema":"vela.problem-packet.v0.1","problem":137,"statement":"We say that $N$ is powerful if whenever $p\\mid N$ we also have $p^2\\mid N$. Let $k\\geq 3$. Can the product of any $k$ consecutive positive integers ever be powerful?","status":"open","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)"}