{"schema":"vela.problem-packet.v0.1","problem":711,"statement":"Let $f(n,m)$ be minimal such that in $(m,m+f(n,m))$ there exist distinct integers $a_1,\\ldots,a_n$ such that $k\\mid a_k$ for all $1\\leq k\\leq n$. Prove that\\[\\max_m f(n,m) \\leq n^{1+o(1)}\\]and that\\[\\max_m (f(n,m)-f(n,n))\\to \\infty.\\]","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)"}