{"schema":"vela.problem-packet.v0.1","problem":1049,"statement":"Let $t>1$ be a rational number. Is\\[\\sum_{n=1}^\\infty\\frac{1}{t^n-1}=\\sum_{n=1}^\\infty \\frac{\\tau(n)}{t^n}\\]irrational, where $\\tau(n)$ counts the divisors of $n$?","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)"}