{"schema":"vela.problem-packet.v0.1","problem":697,"statement":"Let $\\delta(m,\\alpha)$ denote the density of the set of integers which are divisible by some $d\\equiv 1\\pmod{m}$ with $1<d<\\exp(m^\\alpha)$. Does there exist some $\\beta\\in (1,\\infty)$ such that\\[\\lim_{m\\to \\infty}\\delta(m,\\alpha)\\]is $0$ if $\\alpha<\\beta$ and $1$ if $\\alpha>\\beta$?","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)"}