On Cubic Residue Matrices

TL;DR

This paper explores the construction of matrices using cubic residues to achieve specific and predictable determinant values, linking number theory with matrix theory.

Contribution

It introduces a novel approach to matrix construction based on cubic residues, expanding the methods beyond quadratic residues.

Findings

Matrices with predetermined determinants constructed from cubic residues

Connections established between cubic residues and matrix properties

Potential applications in mathematics and statistics

Abstract

The use of quadratic residues to construct matrices with specific determinant values is a familiar problem with connections to many areas of mathematics and statistics. Our research has focused on using cubic residues to construct matrices with interesting and predictable determinants.