Algebraic on Magic Square of Odd Order n

TL;DR

This paper explores the algebraic structure of odd-order magic squares and cubes, establishing their relation to groups and providing a generalized framework for their properties.

Contribution

It introduces a novel algebraic approach linking odd-order magic squares and cubes to group theory, including a unique group construction and generalizations.

Findings

Constructed entries using modulo n for magic squares

Established a unique group associated with odd-order magic squares

Extended results to magic cubes with similar properties

Abstract

This paper aims to address the relation between a magic square of odd order $n$ and a group, and their properties. By the modulo number $n$, we construct entries for each table from initial table of magic square with large number $n^2$. Generalization of the underlying idea is presented, we obtain unique group, and we also prove variants of the main results for magic cubes.