Artin's conjecture on primitive roots

From Number
Jump to: navigation, search

Statement

Infinitude version

Suppose is an integer that is not equal to and is not a perfect square, i.e., is not the square of an integer. Then, there exist infinitely many primes such that is a primitive root modulo .

Density version

Fill this in later

Relation with other conjectures and known facts


Name of conjecture/fact Statement Conditional to ...
Hooley's theorem Artin's conjecture holds for all (special cases of) generalized Riemann hypothesis
Gupta-Ram Murty theorem Artin's conjecture holds for infinitely many Unconditional
Heath-Brown theorem on Artin's conjecture Artin's conjecture holds for all but two exceptional values of . However, no explicit information about the explicit values of Unconditional


External links