Quadratic residues and quartic residues modulo primes
Zhi-Wei Sun

TL;DR
This paper investigates products related to quadratic and quartic residues modulo primes, providing explicit formulas and congruences for these products depending on the prime's residue class.
Contribution
It offers a complete determination of specific product formulas involving quadratic and quartic residues modulo primes, extending known residue characterizations.
Findings
Explicit formulas for products involving quadratic residues.
Characterization of product congruences based on Legendre symbols.
Results for specific quadratic forms modulo primes.
Abstract
In this paper we study some products related to quadratic residues and quartic residues modulo primes. Let be an odd prime and let be any integer. We mainly determine completely the product modulo ; for example, if then where denotes the Legendre symbol. We also determine modulo .
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Taxonomy
TopicsAnalytic Number Theory Research · Advanced Mathematical Theories and Applications · Advanced Mathematical Identities
