{"schema":"vela.problem-packet.v0.1","problem":1112,"statement":"Let $1\\leq d_1<d_2$ and $k\\geq 3$. Does there exist an integer $r$ such that if $B=\\{b_1<\\cdots\\}$ is a lacunary sequence of positive integers with $b_{i+1}\\geq rb_i$ then there exists a sequence of positive integers $A=\\{a_1<\\cdots\\}$ such that\\[d_1\\leq a_{i+1}-a_i\\leq d_2\\]for all $i\\geq 1$ and $(kA)\\cap B=\\emptyset$, where $kA$ is the $k$-fold sumset?","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)"}