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

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.
Pappalardi, F., & Fouad, M.A.M. (2017). On simultaneous primitive roots. ACTA ARITHMETICA, 180(1), 35-43 [10.4064/aa8566-3-2017].
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11590/315402
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