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Integer polynomials that are reducible modulo all primes. (English) Zbl 0603.12002
In this note it is proved that for every positive integer \(n\neq 1\), which is not a prime, there exists a monic irreducible integer polynomial of degree \(n\) such that it is reducible modulo all primes. However, it is known that every monic irreducible polynomial of prime degree remains irreducible modulo infinitely many primes.

MSC:
11C08 Polynomials in number theory
12E05 Polynomials in general fields (irreducibility, etc.)
11S20 Galois theory
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