{"title":"Irreducible Polynomials in Ζ[x] That Are Reducible Modulo All Primes","authors":"Shiv Gupta","doi":"10.4236/OJDM.2019.92006","DOIUrl":null,"url":null,"abstract":"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.","PeriodicalId":61712,"journal":{"name":"离散数学期刊(英文)","volume":"1 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2019-04-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"3","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"离散数学期刊(英文)","FirstCategoryId":"1093","ListUrlMain":"https://doi.org/10.4236/OJDM.2019.92006","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 3
Abstract
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.
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