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Tensor constructions for Euler magic matrices and proper examples of orders 9, 27, 81 and 243
An Euler magic matrix is an integer matrix $M$ satisfying $MM^{\mathsf{T}}=γI$ together with two diagonal square-sum conditions; it is proper when its entry squares are pairwise distinct. M{ü}ller proved that Euler magic matrices exist in every order other than $3$, and that no Euler magic matrix of
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