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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?

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# Generator of ciclic group over finite field

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