On the primitive roots and the generalized Golomb's conjecture

Jiafan Zhang; Xingxing Lv; Jiafan Zhang; Xingxing Lv

doi:10.3934/math.2020361

AIMS Mathematics

2020, Volume 5, Issue 6: 5654-5663. doi: 10.3934/math.2020361

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Research article

On the primitive roots and the generalized Golomb's conjecture

Jiafan Zhang ,
Xingxing Lv ^,

School of Mathematics, Northwest University, Xi'an, Shaanxi, P. R. China

Received: 30 April 2020 Accepted: 22 June 2020 Published: 02 July 2020
MSC : 11A07, 11D85

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].
- primitive roots,
- the estimate for character sums,
- the generalized Golomb's conjecture,
- square-free number
Citation: Jiafan Zhang, Xingxing Lv. On the primitive roots and the generalized Golomb's conjecture[J]. AIMS Mathematics, 2020, 5(6): 5654-5663. doi: 10.3934/math.2020361

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Abstract

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].

References

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