Abstract
<abstract> <p>In this article, we use elementary methods and the estimate for character sums to study the properties of a certain primitive roots modulo <italic>p</italic> (an odd prime), and prove that the generalized Golomb's conjecture is correct in a reduced residue system modulo <italic>p</italic>. This solved an open problem proposed by W. P. Zhang and T. T. Wang in <sup>[<xref ref-type="bibr" rid="b3">3</xref>]</sup>.</p> </abstract>
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