On Grosswald's conjecture on primitive roots

Stephen D. Cohen; Tomás Oliveira e Silva; Tim Trudgian

Stephen D. Cohen ; Tomás Oliveira e Silva ; Tim Trudgian

Acta Arithmetica, Tome 172 (2016), p. 263-270 / Harvested from The Polish Digital Mathematics Library

Résumé

Grosswald’s conjecture is that g(p), the least primitive root modulo p, satisfies g(p) ≤ √p - 2 for all p > 409. We make progress towards this conjecture by proving that g(p) ≤ √p -2 for all $409 < p < 2.5 \times 10^{15}$ and for all $p > 3.38 \times 10^{71}$ .

Publié le : 2016-01-01

Zbl 06545351

EUDML-ID : urn:eudml:doc:286132

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     author = {Stephen D. Cohen and Tom\'as Oliveira e Silva and Tim Trudgian},
     title = {On Grosswald's conjecture on primitive roots},
     journal = {Acta Arithmetica},
     volume = {172},
     year = {2016},
     pages = {263-270},
     zbl = {06545351},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-aa8109-12-2015}
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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) pp. 263-270. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-aa8109-12-2015/