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

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DOI: 10.4236/ojdm.2019.92006    176 Downloads   319 Views
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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.

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Gupta, S. (2019) Irreducible Polynomials in Ζ[x] That Are Reducible Modulo All Primes. Open Journal of Discrete Mathematics, 9, 52-61. doi: 10.4236/ojdm.2019.92006.

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