{"schema":"vela.problem-packet.v0.1","problem":790,"statement":"Let $l(n)$ be maximal such that if $A\\subset\\mathbb{Z}$ with $\\lvert A\\rvert=n$ then there exists a sum-free $B\\subseteq A$ with $\\lvert B\\rvert \\geq l(n)$ - that is, $B$ is such that there are no solutions to\\[a_1=a_2+\\cdots+a_r\\]with $a_i\\in B$ all distinct.Estimate $l(n)$. In particular, is it true that $l(n)n^{-1/2}\\to \\infty$? Is it true that $l(n)< n^{1-c}$ for some $c>0$?","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)"}