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arXiv · 1908.03236

Gaussian Integers, Rings, Finite Fields, and the Magic Square of Squares

Onno Cain
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Abstract

We show the 3 by 3 magic square of squares problem equivalent to solving quartic polynomials with certain factorization constraints over an abelian extension of the rationals. We analyze a particular case in which said extension is assumed to be the Gaussian integers resulting a new search method. Additionally, the magic square of squares is analyzed over finite fields and rings of the form Z/nZ resulting in some conjectures enumerating the rings and finite fields in which a magic square of squares can be constructed. Code is made available.

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Onno Cain. 2019-08-08. Gaussian Integers, Rings, Finite Fields, and the Magic Square of Squares. https://arxiv.org/abs/1908.03236

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