A proper Euler’s magic matrix is an integer $n\times n$ matrix $M\in\mathbb
Z^{n\times n}$ such that $M\cdot M^t=\gamma\cdot I$ for some nonzero constant
$\gamma$, the sum of the squares of the entries along each of the two main
diagonals equals $\gamma$, and the squares of all entries in $M$ are pairwise
distinct. Euler constructed such matrices for $n=4$. In this work, we construct
examples for $n=8$ and prove that no such matrix exists for $n=3$.

Questo articolo esplora i giri e le loro implicazioni.

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