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International Journal of Neutrosophic Science

ISSN
Online: 2690-6805 Print: 2692-6148
Frequency

Continuous publication

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Open access Β· Articles freely available online Β· APC applies after acceptance

International Journal of Neutrosophic Science
Full Length Article

Volume 22 β€’ Issue 2 β€’ PP: 08-14 β€’ 2023

Generating Weak Fuzzy Complex and Anti Weak Fuzzy Complex Integer Solutions for Pythagoras Diophantine Equation π‘ΏπŸ + π’€πŸ = π’πŸ

Abuobida M. A. Alfahal 1* ,
Mohammad Abobala 2 ,
Yaser Ahmad Alhasan 1 ,
Raja Abdullah Abdulfatah 1
1Deanship of the Preparatory Year, Prince Sattam bin Abdulaziz University, Alkharj, Saudi Arabia
2Tishreen University, Department Of Mathematics, Latakia, Syria
* Corresponding Author.
Received: March 27, 2023 Revised: April 25, 2023 Accepted: May 28, 2023

Abstract

In this paper, we find necessary and sufficient conditions for a weak fuzzy complex integer triple (X,Y, Z) to be a pythagoras triple, and for an anti-weak fuzzy complex integer triple   to be a Pythagoras triple  (X,Y, Z), where we prove that the non-linear Fermat's Diophantine equation  has three different types of solutions according to the value of . All types will be solved and discussed in terms of theorems and examples that explains how the algorithms work

Keywords

weak fuzzy complex integer anti-weak fuzzy complex integer Pythagoras triple Pythagoras Diophantine equation.

References

[1] Hatip, A., "An Introduction To Weak Fuzzy Complex Numbers ", Galoitica Journal Of Mathematical Structures and Applications, Vol.3, 2023.

[2] Ahmad, K., " On Some Split-Complex Diophantine Equations", Neoma Journal Of Mathematics and Computer Science, 2023.

[3] Khaldi, A., " A Study On Split-Complex Vector Spaces", Neoma Journal Of Mathematics and Computer Science, 2023.

[4] Merkepci, M., and Abobala, M., " On Some Novel Results About Split-Complex Numbers, The Diagonalization Problem And Applications To Public Key Asymmetric Cryptography", Journal of Mathematics, Hindawi, 2023.

[5] Merkepci, M., and Abobala, M., " Security Model for Encrypting Uncertain Rational Data Units Based on Refined Neutrosophic Integers Fusion and El Gamal Algorithm ", Fusion: Practice and Applications, 2023.

[6] Ali, R., " On The Weak Fuzzy Complex Inner Products On Weak Fuzzy Complex Vector Spaces", Neoma Journal Of Mathematics and Computer Science, 2023.

[7] Hatip, A., "On The Weak Fuzzy Complex Vector Spaces", Galoitica Journal Of Mathematical

Structures And Applications, Vol.3, 2023.

[8] Merkepci, M., Abobala, M., and Allouf, A., " The Applications of Fusion Neutrosophic Number Theory in Public Key Cryptography and the Improvement of RSA Algorithm ", Fusion: Practice and Applications, 2023.

[9] Abobala, M., and Allouf, A., " On A Novel Security Scheme for The Encryption and Decryption Of 2×2 Fuzzy Matrices with Rational Entries Based on The Algebra of Neutrosophic Integers and El-Gamal Crypto-System", Neutrosophic Sets and Systems, vol.54, 2023.

[10] Ben Othman, K., Von Shtawzen, O., Khaldi, A., and Ali, R., "On The Concept Of Symbolic 7-Plithogenic Real Matrices", Pure Mathematics For Theoretical Computer Science, Vol.1, 2023.

[11] Ibrahim, M., and Abobala, M., "An Introduction To Refined Neutrosophic Number Theory", Neutrosophic Sets and Systems, Vol. 45, 2021.

[12] Sankari, H., and Abobala, M., "Neutrosophic Linear Diophantine Equations With two Variables", Neutrosophic Sets and Systems, Vol. 38, pp. 22-30, 2020.

Cite This Article

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Alfahal, Abuobida M. A., Abobala, Mohammad, Alhasan, Yaser Ahmad, Abdulfatah, Raja Abdullah. "Generating Weak Fuzzy Complex and Anti Weak Fuzzy Complex Integer Solutions for Pythagoras Diophantine Equation π‘ΏπŸ + π’€πŸ = π’πŸ." International Journal of Neutrosophic Science, vol. Volume 22, no. Issue 2, 2023, pp. 08-14. DOI: https://doi.org/10.54216/IJNS.220201
Alfahal, A., Abobala, M., Alhasan, Y., Abdulfatah, R. (2023). Generating Weak Fuzzy Complex and Anti Weak Fuzzy Complex Integer Solutions for Pythagoras Diophantine Equation π‘ΏπŸ + π’€πŸ = π’πŸ. International Journal of Neutrosophic Science, Volume 22(Issue 2), 08-14. DOI: https://doi.org/10.54216/IJNS.220201
Alfahal, Abuobida M. A., Abobala, Mohammad, Alhasan, Yaser Ahmad, Abdulfatah, Raja Abdullah. "Generating Weak Fuzzy Complex and Anti Weak Fuzzy Complex Integer Solutions for Pythagoras Diophantine Equation π‘ΏπŸ + π’€πŸ = π’πŸ." International Journal of Neutrosophic Science Volume 22, no. Issue 2 (2023): 08-14. DOI: https://doi.org/10.54216/IJNS.220201
Alfahal, A., Abobala, M., Alhasan, Y., Abdulfatah, R. (2023) 'Generating Weak Fuzzy Complex and Anti Weak Fuzzy Complex Integer Solutions for Pythagoras Diophantine Equation π‘ΏπŸ + π’€πŸ = π’πŸ', International Journal of Neutrosophic Science, Volume 22(Issue 2), pp. 08-14. DOI: https://doi.org/10.54216/IJNS.220201
Alfahal A, Abobala M, Alhasan Y, Abdulfatah R. Generating Weak Fuzzy Complex and Anti Weak Fuzzy Complex Integer Solutions for Pythagoras Diophantine Equation π‘ΏπŸ + π’€πŸ = π’πŸ. International Journal of Neutrosophic Science. 2023;Volume 22(Issue 2):08-14. DOI: https://doi.org/10.54216/IJNS.220201
A. Alfahal, M. Abobala, Y. Alhasan, R. Abdulfatah, "Generating Weak Fuzzy Complex and Anti Weak Fuzzy Complex Integer Solutions for Pythagoras Diophantine Equation π‘ΏπŸ + π’€πŸ = π’πŸ," International Journal of Neutrosophic Science, vol. Volume 22, no. Issue 2, pp. 08-14, 2023. DOI: https://doi.org/10.54216/IJNS.220201
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