Primitive Roots: A Survey
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
Keywordsprimitive root Artin’s conjecture Generalized Riemann Hypothesis
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- J. S. Athreya and L. M. Fidkowski, Number theory, balls in boxes, and the asymptotic uniqueness of maximal discrete order statistics,Integers—The Electronic Journal of Combinatorial Number Theory (http://www.integers-ejcnt.org) 0 (2000), article A3.
- S. Li, On Artin’s conjecture for composite moduli, Ph. D. dissertation, University of Georgia, 1998.Google Scholar
- S. Li and C. Pomerance, On generalizing Artin’s conjecture on primitive roots to composite moduli,J. reine angew. Math., to appear.Google Scholar