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ON THE AVERAGE OF THE LEAST PRIMITIVE ROOT MODULO p

Published online by Cambridge University Press:  01 December 1997

P. D. T. A. ELLIOTT  and
LEO MURATA
P. D. T. A. ELLIOTT
Affiliation:
Department of Mathematics, University of Colorado, Campus Box 395, Boulder, Colorado 80309-0395, USA
LEO MURATA
Affiliation:
Department of Mathematics, Meiji-Gakuin University, 1518 Kamikurata-cho, Totsuka-ku, Yokohama 244, Japan
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Abstract

In this paper we study the value distribution of the least primitive root to a prime modulus, as the modulus varies. For each odd prime number p, we shall denote by g(p) and G(p) the least primitive root and the least prime primitive root (mod p), respectively. Numerical examples show that, in most cases, g(p) and G(p) are very small (cf. §4). We can support this observation by a probabilistic argument [14, §1]. In fact, on the assumption of a good distribution of the primitive residue classes modulo p, we can surmise that

formula here

where π(x) denotes the number of primes not exceeding x.

Type
Notes and Papers
Information
Journal of the London Mathematical Society , Volume 56 , Issue 3 , December 1997 , pp. 435 - 454
Copyright
The London Mathematical Society 1997

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