In number theory, Artin's conjecture on primitive roots states that a given integer a which is not a perfect square and not −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. Although significant progress has been made, the conjecture is still unresolved. In fact, there is no single value of a for which Artin's conjecture is proved.
Read more about Artin's Conjecture On Primitive Roots: Formulation, Example, Proof Attempts
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