{"schema":"vela.problem-packet.v0.1","problem":694,"statement":"Let $f_{\\max}(n)$ be the largest $m$ such that $\\phi(m)=n$, and $f_{\\min}(n)$ be the smallest such $m$, where $\\phi$ is Euler's totient function. Investigate\\[\\max_{n\\leq x}\\frac{f_{\\max}(n)}{f_{\\min}(n)}\\](where the maximum is restricted to those $n$ of the form $n=\\phi(m)$ for some $m$.)","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)"}