Polynomials which are locally reducible

Details Polynomials which are locally reducible Polynomials which are locally reducible

2004-04-04

arxiv.org/abs/math/0404069v1

Mathematics

Number Theory

Scientific paper

Let $K$ be a global field and $n > 1$ an integer. We show $n$ is composite if
and only if there is an irreducible polynomial $f(x) \in K[x]$ of degree $n$
which is reducible $q$-adically for all the primes $q$ of $K$.

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