The Soaisu Structure of the 3×3 Magic Square — Power Sum Coincidences Born from Symmetry

Abstract

This paper analyzes, from multiple perspectives, the soaisu structure hidden within the 3×3 magic square. We begin by clarifying the definition of soaisu and its relationship to the PTE problem, and reveal the soaisu symmetry formed by the rows and columns of the 3×3 magic square. We then apply domino tiling to both the magic square and the natural square, and investigate the soaisu formed by the resulting sum lists. Furthermore, we prove algebraically that the linear maps defined by the rows of the magic square generate infinitely many 3-3 soaisu. Through these results, we demonstrate that the concept of soaisu serves as a powerful tool for analyzing the structure of magic squares.