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].

中文翻译：

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关于原始根和广义的Golomb猜想

在本文中，我们使用基本方法和字符和估计来研究某个原始根模p（奇数素数）的性质，并证明广义Golomb猜想在一个简化的残差系统模p上是正确的。这就解决了由WP Zhang和TT Wang在[3]中提出的开放问题。