Algorithms for Computing Pythagoras Triples and 4-Tiples in Some Neutrosophic Commutative Rings

Abstract

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.