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arXiv 1908.032362019-08-12math.RAmath.NT

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

Onno Cain

备注：: 15 pages

英文摘要：

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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