Geodesic
On Grosswald’s conjecture on primitive roots
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
Acta Arithmetica, Tome 172 (2016) no. 3, pp. 263-270 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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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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     title = {On {Grosswald{\textquoteright}s} conjecture on primitive roots},
     journal = {Acta Arithmetica},
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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

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