{"schema":"vela.problem-packet.v0.1","problem":1122,"statement":"Let $f:\\mathbb{N}\\to \\mathbb{R}$ be an additive function (i.e. $f(ab)=f(a)+f(b)$ whenever $(a,b)=1$). Let\\[A=\\{ n \\geq 1: f(n+1)< f(n)\\}.\\]If $\\lvert A\\cap [1,X]\\rvert =o(X)$ then must $f(n)=c\\log n$ for some $c\\in \\mathbb{R}$?","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)"}