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

1. Dec 6, 2008

### Bourbaki1123

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. Dec 7, 2008

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?