A Partial Residue Categorization of the Magic Square of Squares

2018/09/10 by Christian Woll, Woll, Christian
Computer Science · Engineering · #11A07 #FOS: Mathematics #Graph Labeling and Dimension Problems #Number Theory (math.NT) #graph theory and CDMA systems

paper · pdf · doi:10.48550/arxiv.1809.03067

openalex publication_date 2018/09/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

It is unknown at present whether a magic square of squared integers exists. Such an object is defined to be a 3 by 3 grid of 9 distinct integer squares, such that the entries of each row, column, and two main diagonals sum to the same total. We give a categorization of the residue of the magic square of squares for primes dividing the central entry. The categorization leads to a magic square of square solution over a finite field and, lastly, some conjectures are made regarding the existence of certain residues.

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