Primitive Roots: A Survey

  • Shuguang Li
  • Carl Pomerance
Part of the Developments in Mathematics book series (DEVM, volume 8)


For primes p, the multiplicative group of reduced residues modulo p is cyclic, with cyclic generators being referred to as primitive roots. Here we survey a few results and conjectures on this subject, and we discuss generalizations to arbitrary moduli. A primitive root to a modulus n is a residue coprime to n which generates a cyclic subgroup of maximal order in the group of reduced residues modulo n. 1


primitive root Artin’s conjecture Generalized Riemann Hypothesis 


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Copyright information

© Springer Science+Business Media Dordrecht 2002

Authors and Affiliations

  • Shuguang Li
    • 1
  • Carl Pomerance
    • 2
  1. 1.Department of Mathematics, Natural Sciences DivisionUniversity of Hawaii-HiloHiloUSA
  2. 2.Bell LaboratoriesFundamental Mathematics Research, Mathematics Center, Lucent TechnologiesMurray HillUSA

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