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

Abuobida M. A.; Yaser A.; Raja A.; Rozina

doi:https://doi.org/10.54216/IJNS.200301

Full Length Article

Volume 20 • Issue 3 • PP: 08-14 • 2023

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

Abuobida M. A. Alfahal ^1*

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,

Yaser A. Alhasan ¹

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,

Raja A. Abdulfatah ¹

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,

Rozina Ali ²

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¹Deanship of the Preparatory Year, Prince Sattam bin Abdulaziz University, Alkharj, Saudi Arabia

²Cairo University, department of mathematics, Cairo , Egypt

* Corresponding Author.

DOI https://doi.org/10.54216/IJNS.200301

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

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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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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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