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Steinlein, Heinrich (2017): Fermat's Little Theorem and Gauss Congruence: Matrix Versions and Cyclic Permutations. In: American Mathematical Monthly, Vol. 124, No. 6: pp. 548-553
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Abstract

In recent years, several papers appeared on generalizations of Fermat's little theorem and the Gauss congruence to integer square matrices. We will give simple and intuitive proofs deriving these matrix versions from the corresponding number-theoretic results.