A pr 2 00 4 IRREDUCIBLE POLYNOMIALS WHICH ARE LOCALLY REDUCIBLE EVERYWHERE

@inproceedings{Guralnick2004AP2,
  title={A pr 2 00 4 IRREDUCIBLE POLYNOMIALS WHICH ARE LOCALLY REDUCIBLE EVERYWHERE},
  author={Robert P. Guralnick and Murray M. Schacher and Jack Sonn},
  year={2004}
}
For any positive integer n, there exist polynomials f (x) ∈ Z[x] of degree n which are irreducible over Q and reducible over Q p for all primes p, if and only if n is composite. In fact, this result holds over arbitrary global fields.