{"paper":{"title":"Searching for Disjoint Covering Systems with Precisely One Repeated Modulus","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NT"],"primary_cat":"math.CO","authors_text":"Aviezri S. Fraenkel, Doron Zeilberger, Shalosh B. Ekhad","submitted_at":"2015-11-13T14:37:15Z","abstract_excerpt":"A set of arithmetical sequences $$ a_1\\, (\\bmod{ \\,\\, m_1}) \\quad, \\quad a_2 \\, (\\bmod{\\,\\, m_2}) \\quad, \\quad \\dots \\quad , \\quad a_k \\, (\\bmod{\\,\\,m_k}) \\quad \\quad , $$ with $$ m_1 \\leq m_2 \\leq \\dots \\leq m_k \\quad \\quad , $$ is called a {\\it disjoint covering system} (alias {\\it exact covering system}) if every positive integer belongs to {\\bf exactly} one of the sequences. Mirski, Newman, Davenport and Rado famously proved that the moduli can't all be distinct. In fact the two largest moduli must be equal, i.e. $m_{k-1}=m_k$ This raises the natural question:\"How close can you get to gett"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1511.04293","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"}