Irreducible Polynomials in Ζ[x] That Are Reducible Modulo All Primes

• 作者: Shiv Gupta
• 来源期刊: 离散数学期刊(英文)
• 学科: 数学
• 关键词: IRREDUCIBLE POLYNOMIAL REDUCIBLE POLYNOMIAL GALOIS Theory
• 年，卷（期）: lssxqkyw,（2）
• 页码范围: 52-61
• 页数: 10页
• 分类号: O1

摘要

The polynomial x4+1 is irreducible in Ζ[x] but is locally reducible, that is, it factors modulo p for all primes p. In this paper we investigate this phenomenon and prove that for any composite natural number N there are monic irreducible polynomials in Ζ[x] which are reducible modulo every prime.