{"schema":"vela.problem-packet.v0.1","problem":331,"statement":"Let $A,B\\subseteq \\mathbb{N}$ such that for all large $N$\\[\\lvert A\\cap \\{1,\\ldots,N\\}\\rvert \\gg N^{1/2}\\]and\\[\\lvert B\\cap \\{1,\\ldots,N\\}\\rvert \\gg N^{1/2}.\\]Is it true that there are infinitely many solutions to $a_1-a_2=b_1-b_2\\neq 0$ with $a_1,a_2\\in A$ and $b_1,b_2\\in B$?","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)"}