Geodesic
On simultaneous primitive roots
Mohamed Anwar1 ; Francesco Pappalardi1
1 Dipartimento di Matematica e Fisica Università Roma Tre Largo S. L. Murialdo 1 I-00191 Roma, Italy
Acta Arithmetica, Tome 180 (2017) no. 1, pp. 35-43

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

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.
DOI : 10.4064/aa8566-3-2017
Keywords: given finitely many non zero rational numbers which prove under assumption hypothesis schinzel necessary sufficient conditions existence infinitely many primes modulo which given numbers simultaneously primitive roots stronger result where density primes under consideration computed proved under assumption generalized riemann hypothesis nbsp matthews

Mohamed Anwar 1 ; Francesco Pappalardi 1

1 Dipartimento di Matematica e Fisica Università Roma Tre Largo S. L. Murialdo 1 I-00191 Roma, Italy 
@article{10_4064_aa8566_3_2017,
     author = {Mohamed Anwar and Francesco Pappalardi},
     title = {On simultaneous primitive roots},
     journal = {Acta Arithmetica},
     pages = {35--43},
     publisher = {mathdoc},
     volume = {180},
     number = {1},
     year = {2017},
     doi = {10.4064/aa8566-3-2017},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.4064/aa8566-3-2017/}
}
TY  - JOUR
AU  - Mohamed Anwar
AU  - Francesco Pappalardi
TI  - On simultaneous primitive roots
JO  - Acta Arithmetica
PY  - 2017
SP  - 35
EP  - 43
VL  - 180
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.4064/aa8566-3-2017/
DO  - 10.4064/aa8566-3-2017
LA  - en
ID  - 10_4064_aa8566_3_2017
ER  - 
%0 Journal Article
%A Mohamed Anwar
%A Francesco Pappalardi
%T On simultaneous primitive roots
%J Acta Arithmetica
%D 2017
%P 35-43
%V 180
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.4064/aa8566-3-2017/
%R 10.4064/aa8566-3-2017
%G en
%F 10_4064_aa8566_3_2017
Mohamed Anwar; Francesco Pappalardi. On simultaneous primitive roots. Acta Arithmetica, Tome 180 (2017) no. 1, pp. 35-43. doi: 10.4064/aa8566-3-2017

Cité par Sources :