{"paper":{"title":"A coprimality condition on consecutive values of polynomials","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Carlo Sanna, M\\'arton Szikszai","submitted_at":"2017-04-06T07:57:20Z","abstract_excerpt":"Let $f\\in\\mathbb{Z}[X]$ be quadratic or cubic polynomial. We prove that there exists an integer $G_f\\geq 2$ such that for every integer $k\\geq G_f$ one can find infinitely many integers $n\\geq 0$ with the property that none of $f(n+1),f(n+2),\\dots,f(n+k)$ is coprime to all the others. This extends previous results on linear polynomials and, in particular, on consecutive integers."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1704.01738","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"}