Affiliation:
1. Research Center for Number Theory and Its Applications, Northwest University , Xi’an , Shaanxi , P. R. China
Abstract
Abstract
The main purpose of this article is to use elementary methods and properties of classical Gauss sums to determine identities for the number of residue systems of
a
a
mod
p
p
such that
a
a
,
a
+
a
¯
a+\bar{a}
, and
a
−
a
¯
a-\bar{a}
are all quadratic residues, improving on results of Wang and Lv.
Reference15 articles.
1. T. M. Apostol, Introduction to Analytic Number Theory, Springer-Verlag, New York, 1976.
2. W. P. Zhang and H. L. Li, Elementary Number Theory, Shaanxi Normal University Press, Xi’an, 2013.
3. Z. H. Sun, Consecutive numbers with the same Legendre symbol, Proc. Amer. Math. Soc. 130 (2002), no. 9, 2503–2507, DOI: https://doi.org/10.1090/S0002-9939-02-06600-5.
4. T. T. Wang and X. X. Lv, The quadratic residues and some of their new distribution properties, Symmetry 12 (2020), no. 3, 241, DOI: https://doi.org/10.3390/sym12030421.
5. W. Narkiewicz, Classical Problems in Number Theory, Polish Scientific Publishers, Warszawa, 1986.
Cited by
1 articles.
订阅此论文施引文献
订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献
1. Cubic residues and their new distributive properties;Indian Journal of Pure and Applied Mathematics;2024-02-03