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I describe how to do this generally in my answer to question #16457question #16457 about cyclotomic integers. However, in this particular problem you are probably supposed to use the fact that the divisors of $x^{p^n} - x$ over $\mathbb{F}_p$ are precisely the irreducible polynomials of degree dividing $n$.

I describe how to do this generally in my answer to question #16457 about cyclotomic integers. However, in this particular problem you are probably supposed to use the fact that the divisors of $x^{p^n} - x$ over $\mathbb{F}_p$ are precisely the irreducible polynomials of degree dividing $n$.

I describe how to do this generally in my answer to question #16457 about cyclotomic integers. However, in this particular problem you are probably supposed to use the fact that the divisors of $x^{p^n} - x$ over $\mathbb{F}_p$ are precisely the irreducible polynomials of degree dividing $n$.

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Qiaochu Yuan
Qiaochu Yuan
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I describe how to do this generally in my answer to question #16457 about cyclotomic integers. However, in this particular problem you are probably supposed to use the fact that the divisors of $x^{p^n} - x$ over $\mathbb{F}_p$ are precisely the irreducible polynomials of degree dividing $n$.