{"schema":"vela.problem-packet.v0.1","problem":389,"statement":"Is it true that for every $n\\geq 1$ there is a $k$ such that\\[n(n+1)\\cdots(n+k-1)\\mid (n+k)\\cdots (n+2k-1)?\\]","status":"open","seam":"raw","closureRoutes":[],"obligations":[],"attestations":[],"attempts":[],"velaLean":[],"oeis":[{"id":"A375071","name":"Smallest k such that Product_{i=1..k} (n+i) divides Product_{i=1..k} (n+k+i), or 0 if there is no such k.","terms":"1,5,4,207,206,2475,984,8171,8170,45144,45143,3648830,3648829,7979077,7979076,58068862,58068861,255278295,255278294,10195","url":"https://oeis.org/A375071"}],"generated_note":"derived view; the signed event log is the source of truth (vela check / vela reproduce)"}