Fermat’s little theorem and Euler’s theorem in a class of rings

Abstract

Considering ${\mathbb{Z}}_n$ the ring of integers modulo n, the classical Fermat-Euler theorem establishes the existence of a specific natural number $\phi (n)$ satisfying the following property: $$x^{\phi (n)}=1$$

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.

Keywords:

• Euler Theorem
• Fermat’s Little Theorem
• ring

2020 MATHEMATICS SUBJECT CLASSIFICATION:

• 11A25
• 11T99

Acknowledgment

We appreciate the referee’s comments which improved the manuscript.