Research article

On the primitive roots and the generalized Golomb's conjecture

  • 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].

    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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  • 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].



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  • © 2020 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)
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