{"schema":"vela.problem-packet.v0.1","problem":850,"statement":"Can there exist two distinct integers $x$ and $y$ such that $x,y$ have the same prime factors, $x+1,y+1$ have the same prime factors, and $x+2,y+2$ also have the same prime factors?","status":"open","seam":"raw","closureRoutes":[],"obligations":[],"attestations":[],"attempts":[],"velaLean":[],"oeis":[{"id":"A343101","name":"Pairs of integers (k, m) ordered by m with 1 < k < m such that k has the same prime divisors as m, and, k+1 has the same prime divisors as m+1.","terms":"2,8,6,48,14,224,30,960,75,1215,62,3968,126,16128,254,65024,510,261120,1022,1046528,2046,4190208,4094,16769024,8190,67092","url":"https://oeis.org/A343101"}],"generated_note":"derived view; the signed event log is the source of truth (vela check / vela reproduce)"}