On the Solutions of Fermat's Diophantine Equation in 2-cyclic Refined Neutrosophic Ring of Integers

Abuobida M. A. Alfahal^1,*, Yaser A. Alhasan² , Raja A. Abdulfatah³, Rozina Ali

^1,2,3Deanship of the Preparatory Year, Prince Sattam bin Abdulaziz University, Alkharj, Saudi Arabia

⁴Cairo University, department of mathematics, Cairo , Egypt

Emails: a.alfahal@psau.edu.sa; y.alhasan@psau.edu.sa; r.abdulfatah@psau.edu.sa; Rozyyy123n@gmail.com

^*Corresponding author:  a.alfahal@psau.edu.sa

Abstract

The Diophantine equation  is called the Fermat's Diophantine equation. Its solutions are called general Fermat's triples.The aim of this paper is to study the solutions of Fermat's Diophantine equation in the 2-cyclic refined neutrosophic ring of integers, where we determine all possible solutions of this Diophantine equation, as well as, the special case of Pythagoras triples.

Keywords: 2- cyclic refined Neutrosophic integer; 2-cyclic refined Neutrosophic Fermat's equation; Pythagoras triple