{"schema":"vela.problem-packet.v0.1","problem":235,"statement":"Let $N_k=2\\cdot 3\\cdots p_k$ and $\\{a_1<a_2<\\cdots <a_{\\phi(N_k)}\\}$ be the integers $<N_k$ which are relatively prime to $N_k$. Then, for any $c\\geq 0$, the limit\\[\\frac{\\#\\{ a_i-a_{i-1}\\leq c \\frac{N_k}{\\phi(N_k)} : 2\\leq i\\leq \\phi(N_k)\\}}{\\phi(N_k)}\\]exists and is a continuous function of $c$.","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)"}