{"paper":{"title":"New Lower Bounds for the Least Common Multiples of Arithmetic Progressions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Qianrong Tan, Rongjun Wu, Shaofang Hong","submitted_at":"2012-11-19T15:45:03Z","abstract_excerpt":"For relatively prime positive integers $u_0$ and $r$ and for $0\\le k\\le n$, define $u_k:=u_0+kr$. Let $L_n:={\\rm lcm}(u_0, u_1, ..., u_n)$ and let $a, l\\ge 2$ be any integers. In this paper, we show that, for integers $\\alpha \\geq a$ and $r\\geq \\max(a, l-1)$ and $n\\geq l\\alpha r$, we have $$L_n\\geq u_0r^{(l-1)\\alpha +a-l}(r+1)^n.$$ Particularly, letting $l=3$ yields an improvement to the best previous lower bound on $L_n$ obtained by Hong and Kominers."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1211.4468","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"}