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

Author: Shiv Gupta

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.


Journal: Open Journal of Discrete Mathematics
DOI: 10.4236/ojdm.2019.92006

Paper Id: 91574 (metadata)

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