{"schema":"vela.problem-packet.v0.1","problem":305,"statement":"For integers $1\\leq a<b$ let $D(a,b)$ be the minimal value of $n_k$ such that there exist integers $1\\leq n_1<\\cdots <n_k$ with\\[\\frac{a}{b}=\\frac{1}{n_1}+\\cdots+\\frac{1}{n_k}.\\]Estimate $D(b)=\\max_{1\\leq a<b}D(a,b)$. Is it true that\\[D(b) \\ll b(\\log b)^{1+o(1)}?\\]","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)"}