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On extending Artin's conjecture to composite moduli

Part of:Elementary number theory

Published online by Cambridge University Press:  26 February 2010

Shuguang Li
Shuguang Li
Affiliation:
Department of Mathematics, Natural Sciences Division, University of Hawaii-Hilo, 200 W. Kawili Street, Hilo, HI 96720-4091.
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Extract

It is well known that, if p is prime, the multiplicative group (ℤ/pℤ)* of reduced residues is cyclic. A generator is called a primitive root; there are φ(p − 1) of them, where φ is Euler's function. Thus, (φ(p − 1)/(p−1) is the proportion of primitive roots modulo p in (ℤ/pℤ)*. Elliott has proved that φp − 1)/(p − 1) has a limiting distribution function [2], in the sense that

exists for all real numbers u.

MSC classification

Secondary:11A07: Congruences; primitive roots; residue systems

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Type
Research Article
Information
Mathematika , Volume 46 , Issue 2 , December 1999, pp. 373 - 390
Copyright
Copyright © University College London 1999

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