{"paper":{"title":"Counting Egyptian fractions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Carlo Sanna, Giuseppe Molteni, Lo\\\"ic Greni\\'e, Sandro Bettin","submitted_at":"2019-06-27T22:43:08Z","abstract_excerpt":"For any integer $N \\geq 1$, let $\\mathfrak{E}_N$ be the set of all Egyptian fractions employing denominators less than or equal to $N$. We give upper and lower bounds for the cardinality of $\\mathfrak{E}_N$, proving that $$ \\frac{N}{\\log N} \\prod_{j = 3}^{k} \\log_j N<\\log(\\#\\mathfrak{E}_N) < 0.421\\, N, $$ for any fixed integer $k\\geq 3$ and every sufficiently large $N$, where $\\log_j x$ denotes the $j$-th iterated logarithm of $x$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1906.11986","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"}