{"schema":"vela.problem-packet.v0.1","problem":1192,"statement":"For $A\\subset \\mathbb{N}$ let $f_r(n)$ count the number of solutions to $n=a_1+\\cdots+a_r$ with $a_i\\in A$.Does there exist, for all $r\\geq 2$, a basis $A$ of order $r$ (so that $f_r(n)>0$ for all large $n$) such that\\[\\sum_{n\\leq x}f_r(n)^2 \\ll x\\]for all $x$?","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)"}