{"paper":{"title":"On a conjecture of Erd\\H{o}s about sets without $k$ pairwise coprime integers","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Csaba S\\'andor, Quan-Hui Yang, S\\'andor Z. Kiss","submitted_at":"2017-05-16T14:39:07Z","abstract_excerpt":"Let $\\mathbb{Z}^{+}$ be the set of positive integers. Let $C_{k}$ denote all subsets of $\\mathbb{Z}^{+}$ such that neither of them contains $k + 1$ pairwise coprime integers and $C_k(n)=C_k\\cap \\{1,2,\\ldots,n\\}$. Let $f(n, k) = \\text{max}_{A \\in C_{k}(n)}|A|$, where $|A|$ denotes the number of elements of the set $A$. Let $E_k(n)$ be the set of positive integers not exceeding $n$ which are divisible by at least one of the primes $p_{1}, \\dots{}, p_{k}$, where $p_{i}$ denote the $i$th prime number. In 1962, Erd\\H{o}s conjectured that $f(n, k) = |E(n,k)|$ for every $n \\ge p_{k}$. Recently Chen a"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.05730","kind":"arxiv","version":1},"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"}