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Let $p$, $l$ be prime numbers, $n$ be positive integer. Find the number of irreducible element in $\mathbb {F_p}[x]$ with degree of $l^n$.

I have got the Gauss's formula $\dfrac{1}{n} *\displaystyle\sum_{d|n} µ(n/d)q^d$. But is there any easier method working out this problem?

Thank you!

Chickenmancer
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user771160
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  • Isn't this the same question as this one $4$ days ago? You should not repeat the same question several times. – Dietrich Burde Apr 24 '17 at 14:29
  • @DietrichBurde well, my intention was to find a solution without proving Gauss's formula...the link you referred have I already found before, but all of the 3 answers led to that formula. If you insist this is duplicated, then I will try asking it in another form... – user771160 Apr 24 '17 at 14:30
  • Well, I think this will not be easier. The proof with the Moebius inversion formula is really easy. – Dietrich Burde Apr 24 '17 at 14:32
  • @DietrichBurde ok, thank you for your suggestion. Close it as duplicate. – user771160 Apr 24 '17 at 14:36

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