{"schema":"vela.problem-packet.v0.1","problem":730,"statement":"Are there infinitely many pairs of integers $n\\neq m$ such that $\\binom{2n}{n}$ and $\\binom{2m}{m}$ have the same set of prime divisors?","status":"open","seam":"raw","closureRoutes":[],"obligations":[],"attestations":[],"attempts":[],"velaLean":[],"oeis":[{"id":"A129515","name":"Numbers m such that binomial(2*m, m) has the same prime factors as binomial(2*k, k) for some k > m.","terms":"87,199,237,467,607,967,1127,1319,1483,1903,1943,2012,2047,2287,2348,2359,2464,2479,2495,2507,2623,2645,2719,3349,3467,35","url":"https://oeis.org/A129515"}],"generated_note":"derived view; the signed event log is the source of truth (vela check / vela reproduce)"}