E-resources
Peer reviewed
Open access
-
Josef Al Jumayel; Maretta Sarkis; Hasan Jafar
Neutrosophic sets and systems, 03/2023, Volume: 54Journal Article
The objective of this paper is to answer the open problem proposed about the validity of phi-Euler’s theorem in the refined neutrosophic ring of integers 𝑍(𝐼1,𝐼2) . This work presents an algorithm to compute the values of Euler’s function on refined neutrosophic integers, and it prove that phi-Euler’s theorem is still true in 𝑍(𝐼1,𝐼2). On the other hand, we present a solution for another open question about the solutions of Fermat's Diophantine equation in refined neutrosophic ring of integers, where we determine the solutions of Fermat's Diophantine equation 𝑋 𝑛 + 𝑌 𝑛 = 𝑍 𝑛 ; 𝑛 ≥ 3 in 𝑍(𝐼1,𝐼2).
