Journal of Neutrosophic and Fuzzy Systems JNFS 2771-6449 2771-6430 10.54216/JNFS https://www.americaspg.com/journals/show/1191 2021 2021 University Of Nizwa, Nizwa, Sultanate Of Oman Oliver Von Shtawzen 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 2022 32 36 10.54216/JNFS.030203 https://www.americaspg.com/articleinfo/24/show/1191