{"paper":{"title":"On the equation $ \\boldsymbol{n_1n_2=n_3n_4}$ restricted to factor closed sets","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Michel Weber, Sanying Shi","submitted_at":"2016-07-21T15:37:27Z","abstract_excerpt":"We study the number of solutions $N(B,F)$ of the diophantine equation $n_1n_2=n_3n_4$, where $1\\le n_1\\le B$, $1\\le n_3\\le B$, $n_2, n_4\\in F$ and $F\\subset [1,B]$ is a factor closed set. We study more particularly the case when $F= \\big\\{m=p_1^{\\e_1}\\ldots p_k^{\\e_k}, \\e_j\\in \\{0,1\\}, 1\\le j\\le k\\big\\}$,\n  $p_1,\\ldots,p_k$ being distinct prime numbers."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1607.06366","kind":"arxiv","version":3},"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"}