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Possible Duplicate:
Why $x^{p^n}-x+1$ is irreducible in ${\mathbb{F}_p}$ only when $n=1$ or $n=p=2$

What are the values of $n$ for which the polynomial $$f(x):=x^{p^n}-x+1$$is irreducible over the finite field $\mathbb{F}_p$ ?

I know that for $n=1$ the polynomial is irreducible. Are there any other $n$ for which $f(x)$ is irreducible ?

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    This is a [duplicate](http://math.stackexchange.com/q/122274/11619). Thomas Andrews gives an excellent answer there.2012-09-06
  • 1
    And see [this related question](http://math.stackexchange.com/q/93440/11619) for a specific example.2012-09-06
  • 0
    And [this question](http://math.stackexchange.com/questions/175131/) with several answers (among which one by OP) that show why the polynomial is irreducible for $n=1$.2012-09-06

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