Given finitely many non zero rational numbers which are not $pm1$, 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 in consideration was computed was proved under the assumption of the Generalized Riemann Hypothesis by K. Matthew in 1976.
Pappalardi, F., Fouad, M.A.M. (2017). On simultaneous primitive roots. ACTA ARITHMETICA, 180(1), 35-43 [10.4064/aa8566-3-2017].
On simultaneous primitive roots
Francesco, Pappalardi;Anwar Mohamed Fouad
2017-01-01
Abstract
Given finitely many non zero rational numbers which are not $pm1$, 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 in consideration was computed was proved under the assumption of the Generalized Riemann Hypothesis by K. Matthew in 1976.File in questo prodotto:
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