{"paper":{"title":"On a problem of Sierpinski","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.NT","authors_text":"Jin-Hui Fang, Yong-Gao Chen","submitted_at":"2011-10-21T07:31:51Z","abstract_excerpt":"Let $s\\ge 2$ be an integer. Denote by $\\mu_s$ the least integer so that every integer $\\ell >\\mu_s$ is the sum of exactly $s$ integers $>1 $ which are pairwise relatively prime. In 1964, Sierpi\\'nski asked a determination of $\\mu_s$. Let $p_1=2$, $p_2=3, ...$ be the sequence of consecutive primes and let $\\mu_s = p_2+p_3+...+p_{s+1}+c_s$. P. Erd\\H os proved that there exists an absolute constant $C$ with $-2\\le c_s\\le C$. In this paper, we determine $\\mu_s$ for all $s\\ge 2$. As a corollary, we show that $-2\\le c_s\\le 1100$ and the set of integers $s$ with $\\mu_s= p_2+p_3+... +p_{s+1}+1100$ has"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1110.4714","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}