{"schema":"vela.problem-packet.v0.1","problem":951,"statement":"Let $1<a_1<\\cdots$ be a sequence of real numbers such that\\[\\left\\lvert \\prod_i a_i^{k_i}-\\prod_j a_j^{\\ell_j}\\right\\rvert \\geq 1\\]for every distinct pair of non-negative finitely supported integer tuples $k_i,\\ell_j\\geq 0$. Is it true that\\[\\#\\{ a_i \\leq x\\} \\leq \\pi(x)?\\]","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)"}