Cycles, Eulerian digraphs and the Schönemann-Gauss theorem
DOI:
https://doi.org/10.12775/TMNA.2020.058Keywords
Schönemann-Gauss congruences, characteristic polynomial, Eulerian digraphAbstract
In 19th century, Fermat's little theorem ``$a^p\equiv a({\rm mod}\;p)$ for $a\in\mathbb Z$, $p$ prime'' was generalized in two directions: Schönemann proved a corresponding congruence for the coefficients of monic polynomials, whereas Gauss found a congruence result with $p$ replaced by any $n\in\mathbb N$. Here, we shall give an elementary proof of the common generalization of these two results.References
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