On the primitive roots and the generalized Golomb’s conjecture
In this article, we use elementary methods and the estimate for character sums to study the properties of a certain primitive roots modulo p (an odd prime), and prove that the generalized Golomb’s conjecture is correct in a reduced residue system modulo p. This solved an open problem proposed by W....
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AIMS Press
2020-07-01
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| Series: | AIMS Mathematics |
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| Online Access: | https://www.aimspress.com/article/10.3934/math.2020361/fulltext.html |
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doaj-4b6031ae97f3496bbc5fd86924f72dc32020-11-25T03:02:07ZengAIMS PressAIMS Mathematics2473-69882020-07-01565654566310.3934/math.2020361On the primitive roots and the generalized Golomb’s conjectureJiafan Zhang0Xingxing Lv1School of Mathematics, Northwest University, Xi’an, Shaanxi, P. R. ChinaSchool of Mathematics, Northwest University, Xi’an, Shaanxi, P. R. ChinaIn this article, we use elementary methods and the estimate for character sums to study the properties of a certain primitive roots modulo p (an odd prime), and prove that the generalized Golomb’s conjecture is correct in a reduced residue system modulo p. This solved an open problem proposed by W. P. Zhang and T. T. Wang in [3].https://www.aimspress.com/article/10.3934/math.2020361/fulltext.htmlprimitive rootsthe estimate for character sumsthe generalized golomb’s conjecturesquare-free number |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
Jiafan Zhang Xingxing Lv |
| spellingShingle |
Jiafan Zhang Xingxing Lv On the primitive roots and the generalized Golomb’s conjecture AIMS Mathematics primitive roots the estimate for character sums the generalized golomb’s conjecture square-free number |
| author_facet |
Jiafan Zhang Xingxing Lv |
| author_sort |
Jiafan Zhang |
| title |
On the primitive roots and the generalized Golomb’s conjecture |
| title_short |
On the primitive roots and the generalized Golomb’s conjecture |
| title_full |
On the primitive roots and the generalized Golomb’s conjecture |
| title_fullStr |
On the primitive roots and the generalized Golomb’s conjecture |
| title_full_unstemmed |
On the primitive roots and the generalized Golomb’s conjecture |
| title_sort |
on the primitive roots and the generalized golomb’s conjecture |
| publisher |
AIMS Press |
| series |
AIMS Mathematics |
| issn |
2473-6988 |
| publishDate |
2020-07-01 |
| description |
In this article, we use elementary methods and the estimate for character sums to study the properties of a certain primitive roots modulo p (an odd prime), and prove that the generalized Golomb’s conjecture is correct in a reduced residue system modulo p. This solved an open problem proposed by W. P. Zhang and T. T. Wang in [3]. |
| topic |
primitive roots the estimate for character sums the generalized golomb’s conjecture square-free number |
| url |
https://www.aimspress.com/article/10.3934/math.2020361/fulltext.html |
| work_keys_str_mv |
AT jiafanzhang ontheprimitiverootsandthegeneralizedgolombsconjecture AT xingxinglv ontheprimitiverootsandthegeneralizedgolombsconjecture |
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1724691354667188224 |