: Mathématiques: Artin's conjecture on primitive roots

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Artin's conjecture on primitive roots

In number theory, Artin's conjecture on primitive roots states that a given integer a that is neither a square number nor −1 is a primitive root modulo infinitely many primes p. The conjecture also ascribes an asymptotic density to these primes. This conjectural density equals Artin's constant or a rational multiple thereof.
The conjecture was made by Emil Artin to Helmut Hasse on September 27, 1927, according to the latter's diary. The conjecture is still unresolved as of 2023. In fact, there is no single value of a for which Artin's conjecture is proved.
(Wikipedia, The Free Encyclopedia, https://en.wikipedia.org/wiki/Artin%27s_conjecture_on_primitive_roots)

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