Geodesic
On Grosswald’s conjecture on primitive roots
Stephen D. Cohen1 ; Tomás Oliveira e Silva2 ; Tim Trudgian3
1 School of Mathematics and Statistics University of Glasgow Glasgow G12 8QW, Scotland
2 Departamento de Electrónica, Telecomunicações e Informática Universidade de Aveiro 3810-193 Aveiro, Portugal
3 Mathematical Sciences Institute The Australian National University Canberra, ACT 2601, Australia
Acta Arithmetica, Tome 172 (2016) no. 3, pp. 263-270.

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

Grosswald’s conjecture is that $g(p)$, the least primitive root modulo $p$, satisfies $g(p) \leq \sqrt{p} - 2$ for all $p>409$. We make progress towards this conjecture by proving that $g(p) \leq \sqrt{p} -2$ for all $409 p 2.5\times 10^{15}$ and for all $p > 3.38\times 10^{71}$.
DOI : 10.4064/aa8109-12-2015
Keywords: grosswald conjecture least primitive root modulo satisfies leq sqrt make progress towards conjecture proving leq sqrt nbsp times nbsp times

Stephen D. Cohen 1 ; Tomás Oliveira e Silva 2 ; Tim Trudgian 3

1 School of Mathematics and Statistics University of Glasgow Glasgow G12 8QW, Scotland
2 Departamento de Electrónica, Telecomunicações e Informática Universidade de Aveiro 3810-193 Aveiro, Portugal
3 Mathematical Sciences Institute The Australian National University Canberra, ACT 2601, Australia 
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Stephen D. Cohen; Tomás Oliveira e Silva; Tim Trudgian. On Grosswald’s conjecture on primitive roots. Acta Arithmetica, Tome 172 (2016) no. 3, pp. 263-270. doi : 10.4064/aa8109-12-2015. http://geodesic.mathdoc.fr/articles/10.4064/aa8109-12-2015/

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