{"paper":{"title":"Covering systems where the prime divisors of all moduli are only $2$, $3$, or $5$","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Jonah Klein, Joshua Harrington, Joshua Lowrance, Ognian Trifonov","submitted_at":"2026-05-18T16:51:26Z","abstract_excerpt":"We try to find all quadruples of positive integers $(m,a,b,c)$ with $a \\geq b \\geq c$ such that there exists a distinct covering system with minimum modulus $m$ and least common multiple of the moduli $2^a 3^b 5^c$. We obtain complete description of all such quadruples when $m=2,3,4,5$, or $6$, except when $m=6$ and $b=c=1$. We also show that if the LCM of the moduli has only $2$, $3$, or $5$ as prime divisors, then $m \\leq 9$ and construct a distinct covering system with $m=8$, $a=8$, $b=3$, and $c=2$. When a covering system exists for a quadruple $(m,a,b,c)$ we provide an example. Nonexisten"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.18644","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2605.18644/integrity.json","findings":[],"available":true,"detectors_run":[{"name":"claim_evidence","ran_at":"2026-05-20T00:01:59.181012Z","status":"completed","version":"1.0.0","findings_count":0}],"snapshot_sha256":"ac61f50557c1259a0687e5bb151feb71301f66915f4bc11434dbe7e70bea9d81"},"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"}