Open AccessOn the primitive roots and the generalized Golomb's conjecture
Author(s) -
Jiafan Zhang,
Xingxing Lv
Publication year - 2020
Publication title -
aims mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.329
H-Index - 15
ISSN - 2473-6988
DOI - 10.3934/math.2020361
Subject(s) - modulo , golomb coding , mathematics , conjecture , combinatorics , primitive root modulo n , arithmetic , computer science , image compression , artificial intelligence , image (mathematics) , image processing
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 ] .