{"schema":"vela.problem-packet.v0.1","problem":491,"statement":"Let $f:\\mathbb{N}\\to \\mathbb{R}$ be an additive function (i.e. $f(ab)=f(a)+f(b)$ whenever $(a,b)=1$). If there is a constant $c$ such that $\\lvert f(n+1)-f(n)\\rvert <c$ for all $n$ then must there exist some $c'$ such that\\[f(n)=c'\\log n+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)"}