On the primitive roots and the generalized Golomb’s conjecture

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].

Keywords

• primitive roots
• the estimate for character sums
• the generalized golomb’s conjecture
• square-free number