On Euler's magic matrices of sizes $3$ and $8$

Peter Müller

A proper Euler's magic matrix is an integer $n\times n$ matrix $M\in {\mathbb{Z}}^{n\times n}$ such that $M\cdot M^t={\hat{I}}^3\cdot I$ for some nonzero constant ${\hat{I}}^3$, the sum of the squares o…