International Journal of Neutrosophic Science IJNS 2690-6805 2692-6148 10.54216/IJNS https://www.americaspg.com/journals/show/1619 2020 2020 Deanship of the Preparatory Year, Prince Sattam bin Abdulaziz University, Alkharj, Saudi Arabia Abuobida M. A. Alfahal Deanship of the Preparatory Year, Prince Sattam bin Abdulaziz University, Alkharj, Saudi Arabia Yaser A. Alhasan Deanship of the Preparatory Year, Prince Sattam bin Abdulaziz University, Alkharj, Saudi Arabia Raja A. Abdulfatah Cairo University, department of mathematics, Cairo , Egypt Rozina Ali The Diophantine equation X^n+Y^n=Z^n 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. 2023 2023 08 14 10.54216/IJNS.200301 https://www.americaspg.com/articleinfo/21/show/1619