2
$\begingroup$

Possible Duplicate:
Polynomials irreducible over $\mathbb{Q}$ but reducible over $\mathbb{F}_p$ for every prime $p$

Anyone know an $f\in \mathbb{Z}[x]$ that is irreducible over $\mathbb{Q}$ but whose reduction mod $p$ is reducible over the first three positive primes?

  • 4
    This was discussed recently, e.g., [here](http://math.stackexchange.com/q/77155/742) and [here](http://math.stackexchange.com/q/160847/742) give you examples that are reducible over **all** primes, not just the first three.2012-06-25
  • 0
    @Arturo The question is *not* an exact duplicate of the linked problems. Rather, it is a much simpler case.2012-06-25

3 Answers 3