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Generator of ciclic group over finite field

  1. Mar 18, 2009 #1
    generator of cyclic group over finite field

    Let [tex]F_p[/tex] be a finite field ([tex]p[/tex] 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 [tex](x,y),~x,y\in F_p[/tex]). It is either [tex]p-1[/tex] if -1 is a quadratic non residue, or [tex]p+1[/tex], 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
  2. jcsd
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