{"schema":"vela.problem-packet.v0.1","problem":443,"statement":"Let $m,n\\geq 1$. What is\\[\\# \\{ k(m-k) : 1\\leq k\\leq m/2\\} \\cap \\{ l(n-l) : 1\\leq l\\leq n/2\\}?\\]Can it be arbitrarily large? Is it $\\leq (mn)^{o(1)}$ for all sufficiently large $m,n$?","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)"}