Geodesic
On a generalization of Fermat's little theorem
Izvestiya. Mathematics , Tome 38 (1992) no. 1, pp. 199-201

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We obtain a congruence type arithmetic relation on the set of all triples $(G,H,P)$, where $G$ is a finite group, $H$ is a subgroup, and $P$ is a representation of $G$ by permutations. This relation becomes Fermat's Little Theorem in the case when $G=Z_p$, $H=1$, and $P$ is the regular representation of $G$. 
@article{IM2_1992_38_1_a8,
     author = {S. P. Strunkov},
     title = {On a generalization of {Fermat's} little theorem},
     journal = {Izvestiya. Mathematics },
     pages = {199--201},
     publisher = {mathdoc},
     volume = {38},
     number = {1},
     year = {1992},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_1992_38_1_a8/}
}
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S. P. Strunkov. On a generalization of Fermat's little theorem. Izvestiya. Mathematics , Tome 38 (1992) no. 1, pp. 199-201. http://geodesic.mathdoc.fr/item/IM2_1992_38_1_a8/