On polynomials with roots modulo almost all primes

Research output: Contribution to journalArticlepeer-review

Abstract

Call a monic integer polynomial exceptional if it has a root modulo all but a finite number of primes, but does not have an integer root. We classify all irreducible monic integer polynomials h for which there is an irreducible monic quadratic g such that the product gh is exceptional. We construct exceptional polynomials with all factors of the form Xp−b with p prime and b square-free.
Original languageEnglish
Pages (from-to)251-263
Number of pages13
JournalActa Arithmetica
Volume205
Issue number3
DOIs
Publication statusPublished - 2022

Keywords

  • Galois group
  • polynomial
  • reduction modulo p
  • root

ASJC Scopus subject areas

  • Algebra and Number Theory

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