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On Minimal Sets of Generators for Primitive Roots

Published online by Cambridge University Press:  20 November 2018

Francesco Pappalardi
Francesco Pappalardi*
Affiliation:
Dipartimento di Matematica, Terza Università degli Studi di Roma, Via Corrado Segre, 4, Roma 00146-Italia, e-mail:[email protected]
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Abstract

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A conjecture of Brown and Zassenhaus (see [2]) states that the first log/? primes generate a primitive root (mod p) for almost all primes p. As a consequence of a Theorem of Burgess and Elliott (see [3]) it is easy to see that the first log2p log log4+∊p primes generate a primitive root (mod p) for almost all primes p. We improve this showing that the first log2p/ log log p primes generate a primitive root (mod p) for almost all primes p.

Keywords

11N5611A07sieve theoryprimitive rootsRiemann hypothesis
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 38 , Issue 4 , 01 December 1995 , pp. 465 - 468
Copyright
Copyright © Canadian Mathematical Society 1995

References

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3. Burgess, D. A. and Elliott, P. D. T. A., The average of the least primitive root, Mathematika 15(1968), 39–50.Google Scholar
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