The smallest finite field containing a 3x3 magic square of nine distinct squares is F29; the integer problem is shown equivalent to a quartic factorization condition over abelian extensions.
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Gaussian Integers, Rings, Finite Fields, and the Magic Square of Squares
The smallest finite field containing a 3x3 magic square of nine distinct squares is F29; the integer problem is shown equivalent to a quartic factorization condition over abelian extensions.