International Journal of Neutrosophic Science IJNS 2690-6805 2692-6148 10.54216/IJNS https://www.americaspg.com/journals/show/1633 2020 2020 Department of Mathematics , Gaziantep University, Gaziantep, Turkey Hamiyet Merkepci Department of Mathematics , Gaziantep University, Gaziantep, Turkey Ahmed Hatip This paper is dedicated to study the number theoretical Pythagoras triples\4-tiples problem in several kinds of neutrosophic algebraic systems, where it finds an algorithm to find Pythagoras triples\4-tiples in commutative neutrosophic rings and refined neutrosophic rings too. Besides, the necessary and sufficient condition for a triple\4-tiple to be Pythagoras triple\4-tiple (quadruples) is obtained and proven in term of theorems. In addition, many numerical examples will be illustrated. 2023 2023 107 114 10.54216/IJNS.200310 https://www.americaspg.com/articleinfo/21/show/1633