{"schema":"vela.problem-packet.v0.1","problem":325,"statement":"Let $k\\geq 3$ and $f_{k,3}(x)$ denote the number of integers $\\leq x$ which are the sum of three nonnegative $k$th powers. Is it true that\\[f_{k,3}(x) \\gg x^{3/k}\\]or even $\\gg_\\epsilon x^{3/k-\\epsilon}$?","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)"}