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Primitive roots for every admissible integer base
Proves the infinitude assertion in Artin's primitive root conjecture for every integer a that is neither −1 nor a square. For each such base, at least primes in every sufficiently large interval have primitive root a, with .
Manuscripts in this family · 2
Primitive roots for every admissible integer base
Oct 4, 2026·primitive-roots-all-integer-bases.pdf
We prove the infinitude assertion in Artin's primitive root conjecture: for every integer a that is neither −1 nor a square, there are at least primes in with primitive root a, for some and every sufficiently large x.
Simultaneous primitive roots: a conditional lower bound for prime bases
Oct 4, 2026·simultaneous-primitive-roots-conditional-lower-bound-prime-bases.pdf
For every fixed finite set of distinct positive primes, we prove that at least primes in have every member of the set as a primitive root, for some c > 0 and all sufficiently large x. The result assumes four explicitly stated analytic and sieve inputs from the companion paper on primitive roots for admissible integer bases.