aspg-24-1191-1791482648 20261008180408 American Scientific Publishing Group admin@americaspg.com American Scientific Publishing Group Journal of Neutrosophic and Fuzzy Systems JNFS 2771-6430 2771-6449 2022 3 2 Oliver Von Shtawzen University Of Nizwa, Nizwa, Sultanate Of Oman The objective of this paper is to suggest two new conjectures concerning the invertible elements in 3-cyclic, and 4-cyclic refined neutrosophic rings of integers, where the invertibility condition shows that the solution of some Diophantine equations may determine the classification of the group of units of these algebraic rings. 2022 32 36 1191 https://creativecommons.org/licenses/by/4.0/ 10.54216/JNFS.030203 https://www.americaspg.com/journal/24/article/1191 https://www.americaspg.com/storage/168.pdf