For what values of $n > 1$ and a is $x^n - a$ irreducible in $\mathbb Q[x]$?

$$x^n-a$$

So $n$ is any integer greater than 1, and $a$ is any integer. $a$ being any integer is where I am running into trouble. I have already shown and worked out a proof for this being irreducible when a is prime. Now I am just working through examples, trying to figure out a pattern.

The exercise is asking for application of Eisenstein's Criterion only, so I am assuming that the value of n should have no effect on the irreducibility.

Theorem $\$ Suppose $\,F\,$ is a field and $\:a\in F\:$ and $\:0 < n\in\mathbb Z.\$ Then
$\ \ \ x^n - a\$ is irreducible over $\:F \iff a \not\in F^{\large p}\:$ for all primes $\:p\mid n,\:$ and $\ a\not\in -4\:F^4$ when $\: 4\mid n$
• @James The $\,p$'th powers of elements of $\,F,\,$ i.e. $\,\{c^p\,:\, c\in F\}\ \$ – Bill Dubuque Feb 12 '15 at 2:45