On the parity of the multiplicative order of certain products of integers related to Gauss factorials

TL;DR

This paper investigates the properties of products of integers associated with Gauss factorials, demonstrating that under specific conditions, these products are always quadratic residues, contributing to number theory and factorial-related research.

Contribution

It establishes new conditions under which products related to Gauss factorials are quadratic residues, advancing understanding of their algebraic properties.

Findings

Certain products are always quadratic residues under specified conditions

Provides new criteria for quadratic residuosity of Gauss factorial-related products

Enhances theoretical understanding of multiplicative orders in number theory

Abstract

In this note, we prove that under some conditions, certain products of integers related to Gauss factorials are always quadratic residues.