Quadratic residues and quartic residues modulo primes

Author:

Sun Zhi-Wei1ORCID

Affiliation:

1. Department of Mathematics, Nanjing University, Nanjing 210093, P. R. China

Abstract

In this paper, we study some products related to quadratic residues and quartic residues modulo primes. Let [Formula: see text] be an odd prime and let [Formula: see text] be any integer. We determine completely the product [Formula: see text] modulo [Formula: see text]; for example, if [Formula: see text] then [Formula: see text] where [Formula: see text] denotes the Legendre symbol. We also determine [Formula: see text] modulo [Formula: see text].

Funder

National Natural Science Foundation of China

Publisher

World Scientific Pub Co Pte Lt

Subject

Algebra and Number Theory

Cited by 3 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. A new theorem on quadratic residues modulo primes;Comptes Rendus. Mathématique;2022-09-29

2. Permutations involving squares in finite fields;Electronic Research Archive;2022

3. CUBES IN FINITE FIELDS AND RELATED PERMUTATIONS;Bulletin of the Australian Mathematical Society;2021-07-15

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