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Some Remarks on Artin's Conjecture

Published online by Cambridge University Press:  20 November 2018

M. Ram Murty  and
S. Srinivasan
M. Ram Murty
Affiliation:
Department of Mathematics McGill University, Montreal, Canada
S. Srinivasan
Affiliation:
School of Mathematics Tata Institute of Fundamental Research Homi Bhabha Road Bombay, India
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Abstract

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It is a classical conjecture of E. Artin that any integer a > 1 which is not a perfect square generates the co-prime residue classes (mod ρ) for infinitely many primes ρ. Let E be the set of a > 1, a not a perfect square, for which Artin's conjecture is false. Set E(x) = card(e ∊ E: e ≤ x). We prove that E(x) = 0(log6 x) and that the number of prime numbers in E is at most 6.

Keywords

10H3510H32Artin's conjectureprimitive roots
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 30 , Issue 1 , 01 March 1987 , pp. 80 - 85
Copyright
Copyright © Canadian Mathematical Society 01

References

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