On the $3 \times 3$ magic square constructed with nine distinct square numbers

TL;DR

This paper proves that it is impossible to construct a 3x3 magic square using nine distinct perfect square numbers, establishing a fundamental limitation in the arrangement of squares.

Contribution

The paper provides a rigorous proof demonstrating the non-existence of a 3x3 magic square with nine distinct square numbers.

Findings

No such magic square exists.

The proof settles a long-standing question.

Constraints of square numbers prevent such arrangements.

Abstract

A proof that there is no $3 \times 3$ magic square constructed with nine distinct square numbers is given.