$f(x)$ is irreducible but $f(x^n)$ is reducible

Question

Does there exist an irreducible polynomial $f(x)\in \mathbb{Z}[x]$ with degree greater than one such that for each $n>1$, $f(x^n)$ is reducible?

reducible where? it's always reducible in $\mathbb{C}$, It won't be in $\mathbb{R}$ necessarily. — Matt B., Aug 04 '14 at 13:37

score 2 · Answer 1 · answered Aug 04 '14 at 13:31

2

No. If $f(X)=g(X)h(X)$, then $f(X^n)=g(X^n)h(X^n)$.

answered Aug 04 '14 at 13:31

Hagen von Eitzen

1

I don't think this addresses the question. – Quang Hoang Aug 04 '14 at 13:35
2

Question has been changed. You answered the original one. – drhab Aug 04 '14 at 13:42

1 Answers1