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Irreducible Polynomials in Ζ[x] That Are Reducible Modulo All Primes
Department of Mathematics, West Chester University, West Chester, USA
- 1 Department of Mathematics, West Chester University, West Chester, USA
Open Journal of Discrete Mathematics·Volume 09 (2019)·Pages 52–61·Published 7 March 2019·DOI10.4236/ojdm.2019.92006
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Abstract
The polynomial x 4 +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.
KeywordsIrreducible PolynomialReducible PolynomialGalois Theory
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