International Journal of Neutrosophic Science

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https://doi.org/10.54216/IJNS

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2690-6805ISSN (Online) 2692-6148ISSN (Print)

Volume 22 , Issue 2 , PP: 08-14, 2023 | Cite this article as | XML | Html | PDF | Full Length Article

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 3 , Raja Abdullah Abdulfatah 4

  • 1 Deanship of the Preparatory Year, Prince Sattam bin Abdulaziz University, Alkharj, Saudi Arabia - (a.alfahal@psau.edu.sa)
  • 2 Tishreen University, Department Of Mathematics, Latakia, Syria - (mohammadabobala777@gmail.com)
  • 3 Deanship of the Preparatory Year, Prince Sattam bin Abdulaziz University, Alkharj, Saudi Arabia - (y.alhasan@psau.edu.sa)
  • 4 Deanship of the Preparatory Year, Prince Sattam bin Abdulaziz University, Alkharj, Saudi Arabia - (r.abdulfatah@psau.edu.sa)
  • Doi: https://doi.org/10.54216/IJNS.220201

    Received: March 12, 2023 Revised: June 02, 2023 Accepted: August 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 As :
    M., Abuobida. , Abobala, Mohammad. , Ahmad, Yaser. , Abdullah, Raja. 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. , no. , 2023, pp. 08-14. DOI: https://doi.org/10.54216/IJNS.220201
    M., A. Abobala, M. Ahmad, Y. Abdullah, 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, (), 08-14. DOI: https://doi.org/10.54216/IJNS.220201
    M., Abuobida. Abobala, Mohammad. Ahmad, Yaser. Abdullah, Raja. 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 , no. (2023): 08-14. DOI: https://doi.org/10.54216/IJNS.220201
    M., A. , Abobala, M. , Ahmad, Y. , Abdullah, 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 , () , 08-14 . DOI: https://doi.org/10.54216/IJNS.220201
    M. A. , Abobala M. , Ahmad Y. , Abdullah 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. (): 08-14. DOI: https://doi.org/10.54216/IJNS.220201
    M., A. Abobala, M. Ahmad, Y. Abdullah, 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, vol. , no. , pp. 08-14, 2023. DOI: https://doi.org/10.54216/IJNS.220201