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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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