论文标题
Fermat的Little Therorem和Euler的定理
Fermat's Little Theorem and Euler's Theorem in a class of rings
论文作者
论文摘要
考虑到$ \ mathbb {z} _n $整数Modulo $ n $，经典的Fermat-Euler定理确定了满足以下属性的特定自然数量$φ（n）$：$ x^{φ（n）} all} \ hspace {0.2cm} x \ in \ mathbb {z} _n^*，$属于属于$ \ mathbb {z} _n $的单位组的所有$ x $。在此手稿中，该结果扩展到满足某些温和条件的一类环。
Considering $\mathbb{Z}_n$ the ring of integers modulo $n$, the classical Fermat-Euler theorem establishes the existence of a specific natural number $φ(n)$ satisfying the following property: $ x^{φ(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.
