{"schema":"vela.problem-packet.v0.1","problem":256,"statement":"Let $n\\geq 1$ and $f(n)$ be maximal such that for any integers $1\\leq a_1\\leq \\cdots \\leq a_n$ we have\\[\\max_{\\lvert z\\rvert=1}\\left\\lvert \\prod_{i}(1-z^{a_i})\\right\\rvert\\geq f(n).\\]Estimate $f(n)$ - in particular, is it true that there exists some constant $c>0$ such that\\[\\log f(n) \\gg n^c?\\]","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)"}