{"paper":{"title":"An irreducibility criterion for integer polynomials","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AC","authors_text":"Anuj Jakhar, Neeraj Sangwan","submitted_at":"2016-12-06T09:03:48Z","abstract_excerpt":"Let $f(x) = \\sum\\limits _{i=0}^{n} a_i x^i $ be a polynomial with coefficients from the ring $\\mathbb{Z}$ of integers satisfying either $(i)$ $0 < a_0 \\leq a_{1} \\leq \\cdots \\leq a_{k-1} < a_{k} < a_{k+1} \\leq \\cdots \\leq a_n$ for some $k$, $0 \\leq k \\leq n-1$; or $(ii)$ $|a_n| > |a_{n-1}| + \\cdots + |a_{0}|$ with $a_0 \\neq 0$. In this paper, it is proved that if $|a_n|$ or $|f(m)|$ is a prime number for some integer $m$ with $|m|\\geq 2 $ then the polynomial $f(x)$ is irreducible over $\\mathbb{Z}$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1612.01712","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"}