{"schema":"vela.problem-packet.v0.1","problem":318,"statement":"Let $A\\subseteq \\mathbb{N}$ be an infinite arithmetic progression and $f:A\\to \\{-1,1\\}$ be a non-constant function. Must there exist a finite non-empty $S\\subset A$ such that\\[\\sum_{n\\in S}\\frac{f(n)}{n}=0?\\]What about if $A$ is an arbitrary set of positive density? What if $A$ is the set of squares excluding $1$?","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)"}