{"schema":"vela.problem-packet.v0.1","problem":885,"statement":"For integer $n\\geq 1$ we define the factor difference set of $n$ by\\[D(n) = \\{\\lvert a-b\\rvert : n=ab\\}.\\]Is it true that, for every $k\\geq 1$, there exist integers $N_1<\\cdots<N_k$ such that\\[\\lvert \\cap_i D(N_i)\\rvert \\geq k?\\]","status":"open","seam":"raw","closureRoutes":[],"obligations":[],"attestations":[],"attempts":[{"id":"att_1f0a256511fd0b14","kind":"dead_end","claim":"attempted via frontier 'difference/covering' (transfer_strength=none) -> no_progress","grade":"honest_null","gateStatus":"needs_verification","superseded":false}],"velaLean":[],"oeis":[],"generated_note":"derived view; the signed event log is the source of truth (vela check / vela reproduce)"}