{"paper":{"title":"On Irreducible Polynomials of the Form $b(x^d)$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Palash Sarkar, Shashank Singh","submitted_at":"2016-04-28T05:21:40Z","abstract_excerpt":"Let $p$ be a prime and $b(x)$ be an irreducible polynomial of degree $k$ over $\\mathbb{F}_p$. Let $d\\geq 1$ be an integer. Consider the following question: Is $b(x^d)$ irreducible? We derive necessary conditions for $b(x^d)$ to be irreducible. Further, when the necessary conditions are satisfied, we obtain the probability for $b(x^d)$ to be irreducible."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1604.08303","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"}