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On simultaneous primitive roots

Volume 180 / 2017

Mohamed Anwar, Francesco Pappalardi Acta Arithmetica 180 (2017), 35-43 MSC: Primary 11N64; Secondary 11A07, 11R45. DOI: 10.4064/aa8566-3-2017 Published online: 1 August 2017

Abstract

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.

Authors

  • Mohamed AnwarDipartimento di Matematica e Fisica
    Università Roma Tre
    Largo S. L. Murialdo 1
    I-00191 Roma, Italy
    e-mail
  • Francesco PappalardiDipartimento di Matematica e Fisica
    Università Roma Tre
    Largo S. L. Murialdo 1
    I-00191 Roma, Italy
    e-mail

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