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arXiv · 2012.06949

Fermat's Little Theorem and Euler's Theorem in a class of rings

Fernanda D. de Melo Hernandez·César A. Hernández Melo·Horacio Tapia-Recillas
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Abstract

Considering $\mathbb{Z}_n$ the ring of integers modulo $n$, the classical Fermat-Euler theorem establishes the existence of a specific natural number $\varphi(n)$ satisfying the following property: $ x^{\varphi(n)}=1%\hspace{1.0cm}\text{for all}\hspace{0.2cm}x\in \mathbb{Z}_n^*, $ for all $x$ belonging to the group of units of $\mathbb{Z}_n$. In this manuscript, this result is extended to a class of rings that satisfies some mild conditions.

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Fernanda D. de Melo Hernandez, César A. Hernández Melo, Horacio Tapia-Recillas. 2020-12-13. Fermat's Little Theorem and Euler's Theorem in a class of rings. https://arxiv.org/abs/2012.06949

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