TITLE:
Irreducible Polynomials in Ζ[x] That Are Reducible Modulo All Primes
AUTHORS:
Shiv Gupta
KEYWORDS:
Irreducible Polynomial, Reducible Polynomial, Galois Theory
JOURNAL NAME:
Open Journal of Discrete Mathematics,
Vol.9 No.2,
April
2,
2019
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.