# Generator of ciclic group over finite field

1. Mar 18, 2009

### jegan

generator of cyclic group over finite field

Let $$F_p$$ be a finite field ($$p$$ is prime). Let us consider the unite circle over this field. We know the number of rational points on this circle (i.e. the points $$(x,y),~x,y\in F_p$$). It is either $$p-1$$ if -1 is a quadratic non residue, or $$p+1$$, otherwise.
Clearly this points forms a cyclic group (under multiplication of complex numbers). My question, is there any way/algorithm to find the generator for this group?

Last edited: Mar 18, 2009