On simultaneous primitive roots
Volume 180 / 2017
Acta Arithmetica 180 (2017), 35-43 MSC: Primary 11N64; Secondary 11A07, 11R45. DOI: 10.4064/aa8566-3-2017 Published online: 1 August 2017
Given finitely many non-zero rational numbers which are not $\pm 1$, we prove, under the assumption of Hypothesis H of Schinzel, necessary and sufficient conditions for the existence of infinitely many primes modulo which all the given numbers are simultaneously primitive roots. A stronger result where the density of the primes under consideration was computed was proved under the assumption of the Generalized Riemann Hypothesis by K. Matthews in 1976.