1
Deanship of the Preparatory Year, Prince Sattam bin Abdulaziz University, Alkharj, Saudi Arabia
(a.alfahal@psau.edu.sa)
2
Deanship of the Preparatory Year, Prince Sattam bin Abdulaziz University, Alkharj, Saudi Arabia
(y.alhasan@psau.edu.sa)
3
Deanship of the Preparatory Year, Prince Sattam bin Abdulaziz University, Alkharj, Saudi Arabia
(r.abdulfatah@psau.edu.sa)
4
Cairo University, department of mathematics, Cairo , Egypt
(Rozyyy123n@gmail.com)
Abstract :
The Diophantine equation X^n+Y^n=Z^n is called the Fermat's Diophantine equation. Its solutions are called general Fermat's triples.The aim of this paper is to study the solutions of Fermat's Diophantine equation in the 2-cyclic refined neutrosophic ring of integers, where we determine all possible solutions of this Diophantine equation, as well as, the special case of Pythagoras triples.
Keywords :
2- cyclic refined Neutrosophic integer; 2-cyclic refined Neutrosophic Fermat's equation; Pythagoras triple
References :
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[12] Smarandache, F., "Symbolic Neutrosophic Theory", EuropaNova asbl, Bruxelles, 2015.
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[14] Merkepci, H., and Abobala, M., " The Application of AH-isometry In The Study Of Neutrosophic Conic Sections", Galoitica Journal Of Mathematical Structures And Applications, Vol.2, 2022.
[15] Abobala, M., and Zeina, M.B., " A Study Of Neutrosophic Real Analysis By Using One Dimensional Geometric AH-Isometry", Galoitica Journal Of Mathematical Structures And Applications, Vol.3, 2023
[16] Hatip, A., "An Introduction To Weak Fuzzy Complex Numbers ", Galoitica Journal Of Mathematical Structures and Applications, Vol.3, 2023
[17] Kandasamy, V.W.B., and Smarandache, F., "Some Neutrosophic Algebraic Structures and Neutrosophic N-Algebraic Structures", Hexis, Phonex, Arizona 2006.
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[19] Sadiq, B., " A Contribution To The Group Of Units' Problem In Some 2-Cyclic Refined Neutrosophic Rings", International Journal Of Neutrosophic Science, 2022.
Style | # |
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MLA | Abuobida M. A. Alfahal, Yaser A. Alhasan, Raja A. Abdulfatah, Rozina Ali. "On the Solutions of Fermat's Diophantine Equation in 2-cyclic Refined Neutrosophic Ring of Integers." International Journal of Neutrosophic Science, Vol. 20, No. 3, 2023 ,PP. 08-14 (Doi : https://doi.org/10.54216/IJNS.200301) |
APA | Abuobida M. A. Alfahal, Yaser A. Alhasan, Raja A. Abdulfatah, Rozina Ali. (2023). On the Solutions of Fermat's Diophantine Equation in 2-cyclic Refined Neutrosophic Ring of Integers. Journal of International Journal of Neutrosophic Science, 20 ( 3 ), 08-14 (Doi : https://doi.org/10.54216/IJNS.200301) |
Chicago | Abuobida M. A. Alfahal, Yaser A. Alhasan, Raja A. Abdulfatah, Rozina Ali. "On the Solutions of Fermat's Diophantine Equation in 2-cyclic Refined Neutrosophic Ring of Integers." Journal of International Journal of Neutrosophic Science, 20 no. 3 (2023): 08-14 (Doi : https://doi.org/10.54216/IJNS.200301) |
Harvard | Abuobida M. A. Alfahal, Yaser A. Alhasan, Raja A. Abdulfatah, Rozina Ali. (2023). On the Solutions of Fermat's Diophantine Equation in 2-cyclic Refined Neutrosophic Ring of Integers. Journal of International Journal of Neutrosophic Science, 20 ( 3 ), 08-14 (Doi : https://doi.org/10.54216/IJNS.200301) |
Vancouver | Abuobida M. A. Alfahal, Yaser A. Alhasan, Raja A. Abdulfatah, Rozina Ali. On the Solutions of Fermat's Diophantine Equation in 2-cyclic Refined Neutrosophic Ring of Integers. Journal of International Journal of Neutrosophic Science, (2023); 20 ( 3 ): 08-14 (Doi : https://doi.org/10.54216/IJNS.200301) |
IEEE | Abuobida M. A. Alfahal, Yaser A. Alhasan, Raja A. Abdulfatah, Rozina Ali, On the Solutions of Fermat's Diophantine Equation in 2-cyclic Refined Neutrosophic Ring of Integers, Journal of International Journal of Neutrosophic Science, Vol. 20 , No. 3 , (2023) : 08-14 (Doi : https://doi.org/10.54216/IJNS.200301) |