Universal Closed-Form Construction for Odd-Order Magic Squares (The Mamzeris Method)

This paper presents the Mamzeris Method for constructing associative magic squares of odd order, including, for the first time, the universal closed-form formula for instantly computing the value of any cell given its coordinates (x, y) and the order N of the square. Developed by Smaragdos (Marios) Mamzeris, the work substantially extends the prior algorithmic approach (see Zenodo DOI: 10.5281/zenodo.17203383), previously developed by the author, providing a rigorous, explicit mathematical formula as well as detailed worked examples, notational standards, and permutation enumeration.

This document is designed for mathematicians, educators, and enthusiasts, and contains both algorithmic instructions and direct formula computation methods. Historical context, comparison with prior work, and references for further reading are included.

Keywords: magic squares, combinatorics, closed-form formula, permutations, odd order, Mamzeris Method