{"title":"A divisor problem for polynomials","authors":"Benjamin Klahn","doi":"10.4064/aa200528-21-4","DOIUrl":null,"url":null,"abstract":"We characterize all monic polynomials f(x) ∈ Z[x] that have the property that f(p) | f(p), for all sufficiently large primes p ≥ N(f). We also give necessary conditions and a sufficient condition for monic polynomials f(x) ∈ Z[x] to satisfy f(p) | f(p) for all primes p.","PeriodicalId":37888,"journal":{"name":"Acta Arithmetica","volume":" ","pages":""},"PeriodicalIF":0.5000,"publicationDate":"2022-02-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Acta Arithmetica","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.4064/aa200528-21-4","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
Abstract
We characterize all monic polynomials f(x) ∈ Z[x] that have the property that f(p) | f(p), for all sufficiently large primes p ≥ N(f). We also give necessary conditions and a sufficient condition for monic polynomials f(x) ∈ Z[x] to satisfy f(p) | f(p) for all primes p.
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