{"schema":"vela.problem-packet.v0.1","problem":1001,"statement":"Let $S(N,A,c)$ be the measure of the set of those $\\alpha\\in (0,1)$ such that\\[\\left\\lvert \\alpha-\\frac{x}{y}\\right\\rvert< \\frac{A}{y^2}\\]for some $N\\leq y\\leq cN$ and $(x,y)=1$. Does\\[\\lim_{N\\to \\infty}S(N,A,c)=f(A,c)\\]exist? What is its explicit form?","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)"}