{"paper":{"title":"The least common multiple of consecutive quadratic progression terms","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Guoyou Qian, Shaofang Hong","submitted_at":"2012-08-25T09:06:43Z","abstract_excerpt":"Let $k$ be an arbitrary given positive integer and let $f(x)\\in {\\mathbb Z}[x]$ be a quadratic polynomial with $a$ and $D$ as its leading coefficient and discriminant, respectively. Associated to the least common multiple ${\\rm lcm}_{0\\le i\\le k}\\{f(n+i)\\}$ of any $k+1$ consecutive terms in the quadratic progression $\\{f(n)\\}_{n\\in \\mathbb{N}^*}$, we define the function $g_{k, f}(n):=(\\prod_{i=0}^{k}|f(n+i)|)/{\\rm lcm}_{0\\le i\\le k}\\{f(n+i)\\}$ for all integers $n\\in \\mathbb{N}^*\\setminus Z_{k, f}$, where $Z_{k,f}:=\\bigcup_{i=0}^k\\{n\\in \\mathbb{N}^*: f(n+i)=0\\}$. In this paper, we first show th"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1208.5119","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"}