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

Abstract

Considering 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:for all x belonging to the group of units of Z n . In this manuscript, this result is extended to a class of rings that satisfies some mild conditions.

Proofs, Generalizations and Applications of Fermat’s Little Theorem

“…In Ref. [7], the authors generalized Euler's totient theorem to rings that has ideals {𝑁 1 , … , 𝑁 𝑟 } that the statements below hold:…”