{"schema":"vela.problem-packet.v0.1","problem":323,"statement":"Let $1\\leq m\\leq k$ and $f_{k,m}(x)$ denote the number of integers $\\leq x$ which are the sum of $m$ many nonnegative $k$th powers. Is it true that\\[f_{k,k}(x) \\gg_\\epsilon x^{1-\\epsilon}\\]for all $\\epsilon>0$? Is it true that if $m<k$ then\\[f_{k,m}(x) \\gg x^{m/k}\\]for sufficiently large $x$?","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)"}