Abstract

Artin, in 1927, conjectured that for any given non-zero integer a other than — 1 or a perfect square there exist infinitely many primes for which a is a primitive root. He also conjectured that the number of primes not exceeding x, denoted by Na(x), for which a is a primitive root is given by the asymptotic formulawhere A(a) is a constant depending on a.

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