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International Journal of Neutrosophic Science

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Online: 2690-6805 Print: 2692-6148
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Open access journal. All articles are freely available online with no APC.

International Journal of Neutrosophic Science
Full Length Article

Volume 20Issue 3PP: 08-14 • 2023

On the Solutions of Fermat's Diophantine Equation in 2-cyclic Refined Neutrosophic Ring of Integers

Abuobida M. A. Alfahal 1* ,
Yaser A. Alhasan 1 ,
Raja A. Abdulfatah 1 ,
Rozina Ali 2
1Deanship of the Preparatory Year, Prince Sattam bin Abdulaziz University, Alkharj, Saudi Arabia
2Cairo University, department of mathematics, Cairo , Egypt
* Corresponding Author.
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Open Access & Copyright

© 2023 The Author(s). Published by ASPG. This article is licensed under the Creative Commons Attribution 4.0 International License (CC BY 4.0).

Received: August 20, 2022 Accepted: March 02, 2023

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&nbsp

References

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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

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Cite This Article

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Alfahal, Abuobida M. A., Alhasan, Yaser A., Abdulfatah, Raja A., Ali, Rozina. "On the Solutions of Fermat's Diophantine Equation in 2-cyclic Refined Neutrosophic Ring of Integers." International Journal of Neutrosophic Science, vol. Volume 20, no. Issue 3, 2023, pp. 08-14. DOI: https://doi.org/10.54216/IJNS.200301
Alfahal, A., Alhasan, Y., Abdulfatah, R., Ali, R. (2023). On the Solutions of Fermat's Diophantine Equation in 2-cyclic Refined Neutrosophic Ring of Integers. International Journal of Neutrosophic Science, Volume 20(Issue 3), 08-14. DOI: https://doi.org/10.54216/IJNS.200301
Alfahal, Abuobida M. A., Alhasan, Yaser A., Abdulfatah, Raja A., Ali, Rozina. "On the Solutions of Fermat's Diophantine Equation in 2-cyclic Refined Neutrosophic Ring of Integers." International Journal of Neutrosophic Science Volume 20, no. Issue 3 (2023): 08-14. DOI: https://doi.org/10.54216/IJNS.200301
Alfahal, A., Alhasan, Y., Abdulfatah, R., Ali, R. (2023) 'On the Solutions of Fermat's Diophantine Equation in 2-cyclic Refined Neutrosophic Ring of Integers', International Journal of Neutrosophic Science, Volume 20(Issue 3), pp. 08-14. DOI: https://doi.org/10.54216/IJNS.200301
Alfahal A, Alhasan Y, Abdulfatah R, Ali R. On the Solutions of Fermat's Diophantine Equation in 2-cyclic Refined Neutrosophic Ring of Integers. International Journal of Neutrosophic Science. 2023;Volume 20(Issue 3):08-14. DOI: https://doi.org/10.54216/IJNS.200301
A. Alfahal, Y. Alhasan, R. Abdulfatah, R. Ali, "On the Solutions of Fermat's Diophantine Equation in 2-cyclic Refined Neutrosophic Ring of Integers," International Journal of Neutrosophic Science, vol. Volume 20, no. Issue 3, pp. 08-14, 2023. DOI: https://doi.org/10.54216/IJNS.200301
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