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Artin's conjecture on the average
Published online by Cambridge University Press: 26 February 2010
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It was conjectured by Artin [1] that each non-zero integer a unequal to +1, −1 or a perfect square is a primitive root for infinitely many primes p. More precisely, denoting by Na(x) the number of primes p ≤ x for which a is a primitive root, he conjectured that
where c(a) is a positive constant. This conjecture has recently been proved by C. Hooley [2] under the assumption that the Riemann hypothesis holds for fields of the type .
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