{"schema":"vela.problem-packet.v0.1","problem":785,"statement":"Let $A,B\\subseteq \\mathbb{N}$ be infinite sets such that $A+B$ contains all large integers. Let $A(x)=\\lvert A\\cap [1,x]\\rvert$ and similarly for $B(x)$. Is it true that if $A(x)B(x)\\sim x$ then\\[A(x)B(x)-x\\to \\infty\\]as $x\\to \\infty$?","status":"solved","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)"}