{"paper":{"title":"Primitive prime divisors and the $n$-th cyclotomic polynomial","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Alice C. Niemeyer, Cheryl E. Praeger, Frank L\\\"ubeck, S. P. Glasby","submitted_at":"2015-04-10T09:10:38Z","abstract_excerpt":"Primitive prime divisors play an important role in group theory and number theory. We study a certain number theoretic quantity, called $\\Phi^*_n(q)$, which is closely related to the cyclotomic polynomial $\\Phi_n(x)$ and to primitive prime divisors of $q^n-1$. Our definition of $\\Phi^*_n(q)$ is novel, and we prove it is equivalent to the definition given by Hering. Given positive constants $c$ and $k$, we give an algorithm for determining all pairs $(n,q)$ with $\\Phi^*_n(q)\\le cn^k$. This algorithm is used to extend (and correct) a result of Hering which is useful for classifying certain famil"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1504.02598","kind":"arxiv","version":4},"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"}