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Licensed Unlicensed Requires Authentication Published by De Gruyter November 30, 2012

Artin's Primitive Root Conjecture – A Survey

Pieter Moree
From the journal Integers


One of the first concepts one meets in elementary number theory is that of the multiplicative order. We give a survey of the literature on this topic emphasizing the Artin primitive root conjecture (1927). The first part of the survey is intended for a rather general audience and rather colloquial, whereas the second part is intended for number theorists and ends with several open problems. The contributions in the survey on `elliptic Artin' are due to Alina Cojocaru. Wojciec Gajda wrote a section on `Artin for K-theory of number fields,' and Hester Graves (together with me) on `Artin's conjecture and Euclidean domains.'

Received: 2011-06-07
Revised: 2012-06-29
Accepted: 2012-07-27
Published Online: 2012-11-30
Published in Print: 2012-12-01

© 2012 by Walter de Gruyter Berlin Boston

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