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Number of primative roots in finite fields of order p^n

  1. Dec 6, 2008 #1
    Is it true as it is for finite fields of order p^1, that the number of primitive roots of fields of order p^n is the euler totient of (P^n-1)? If not is there a different rule for the number?
     
  2. jcsd
  3. Dec 7, 2008 #2
    Well, say you have a finite field F = GF(pn). Then F*, the multiplicative group of units of F, is cyclic and has order pn - 1. But the number of generators of a cyclic group G is φ(|G|), so F* has φ(pn - 1) generators, i.e. F has φ(pn - 1) primitive elements.

    Is that what you were asking?
     
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