Galoitica: Journal of Mathematical Structures and Applications GJMSA 2834-5568 10.54216/GJSMA https://www.americaspg.com/journals/show/1300 2022 2022 Imam Kadhum College, Iraq A. Alrida .. Islamic University Of Gaza, Palestine Katy D. Ahmad Cairo University, Egypt Rozina Ali The objective of this paper is to present a new class of Diophantine equations derived from the group of units problem of n-cyclic refined neutrosophic rings of integers by using homomorphisms between these rings and a finite Cartesian product ring of Z with itself. Also, this work provides many examples about this class and its solvability as a new application of neutrosophic algebraic structures in number theory. 2022 2022 36 41 10.54216/GJMSA.010103 https://www.americaspg.com/articleinfo/33/show/1300