Journal of Neutrosophic and Fuzzy Systems

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https://doi.org/10.54216/JNFS

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Volume 1 , Issue 2 , PP: 55-60, 2021 | Cite this article as | XML | Html | PDF | Full Length Article

A Short Note On The Solutions Of Fermat's Diohantine Equation In Some Neutrosophic Rings

Katy D. Ahmad 1 * , Mikail Bal 2 , Malath Aswad 3

  • 1 Islamic University Of Gaza, Palestine - (katyon765@gmail.com)
  • 2 Gaziantep University, Turkey - (mikailbal46@hotmail.com)
  • 3 Malath Aswad, Albaath university, Syria - (malaz.aswad@yahoo.com)
  • Doi: https://doi.org/10.54216/JNFS.010201

    Received: September 11, 2021 Accepted: December 25, 2021
    Abstract

    This paper is dedicated to study the concept of Fermat's triples in rings. Also, it determines the possible Fermat's triples in the neutrosophic ring of integers Z(I). Also, it discussed these triples in several finite commutative rings such as Zn.

     

    Keywords :

    Neutrosophic Ring, Fermat's Diophantine equation, Neutrosophic Integer

    References

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    [3] Das, R., Smarandache, F., and Tripathy, B., "Neutrosophic Fuzzy Matrices and Some Algebraic Operations", Neutrosophic Sets and Systems, Vol. 32, pp. 401-409, 2020 

    [4] Kandasamy, V.W.B., and Smarandache, F., "Some Neutrosophic Algebraic Structures and Neutrosophic N-Algebraic Structures", Hexis, Phonex, Arizona, 2006.

    [5] Agboola, A.A.A., Akinola, A.D., and Oyebola, O.Y., " Neutrosophic Rings I" , International J.Mathcombin, Vol 4,pp 1-14. 2011

     [6] Abobala, M., "On The Characterization of Maximal and Minimal Ideals In Several Neutrosophic Rings", Neutrosophic Sets and Systems, Vol. 45, 2021.

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    [9] Abobala, M., "A Study Of Nil Ideals and Kothe's Conjecture In Neutrosophic Rings", International Journal of Mathematics and Mathematical Sciences, hindawi, 2021

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    [11] Abobala, M., Bal, M., and Hatip, A.," A Review On Recent Advantages In Algebraic Theory Of Neutrosophic Matrices", International Journal of Neutrosophic Science, Vol. 17, 2021.

    [12] Hatip, A., and Olgun, N.,  "On Refined Neutrosophic R-Module", International Journal of Neutrosophic Science, Vol. 7, pp.87-96. 2020.

     [13] Hajjari, A., and Ali, R., " A Contribution To Kothe's Conjecture In Refined Neutrosophic Rings", International Journal of Neutrosophic Science", Vol. 16, 2021.

     [14] Olgun, N., Hatip, A., Bal, M., and Abobala, M., " A Novel Approach To Necessary and Sufficient Conditions For The Diagonalization of Refined Neutrosophic Matrices", International Journal of Neutrosophic Science, Vol. 16, pp. 72-79, 2021.

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    [16] Wiles, A., "Modular Elliptic Curves and Fermat's Last Theorem", Annals Of Mathematics, 1995.

    Cite This Article As :
    D., Katy. , Bal, Mikail. , Aswad, Malath. A Short Note On The Solutions Of Fermat's Diohantine Equation In Some Neutrosophic Rings. Journal of Neutrosophic and Fuzzy Systems, vol. , no. , 2021, pp. 55-60. DOI: https://doi.org/10.54216/JNFS.010201
    D., K. Bal, M. Aswad, M. (2021). A Short Note On The Solutions Of Fermat's Diohantine Equation In Some Neutrosophic Rings. Journal of Neutrosophic and Fuzzy Systems, (), 55-60. DOI: https://doi.org/10.54216/JNFS.010201
    D., Katy. Bal, Mikail. Aswad, Malath. A Short Note On The Solutions Of Fermat's Diohantine Equation In Some Neutrosophic Rings. Journal of Neutrosophic and Fuzzy Systems , no. (2021): 55-60. DOI: https://doi.org/10.54216/JNFS.010201
    D., K. , Bal, M. , Aswad, M. (2021) . A Short Note On The Solutions Of Fermat's Diohantine Equation In Some Neutrosophic Rings. Journal of Neutrosophic and Fuzzy Systems , () , 55-60 . DOI: https://doi.org/10.54216/JNFS.010201
    D. K. , Bal M. , Aswad M. [2021]. A Short Note On The Solutions Of Fermat's Diohantine Equation In Some Neutrosophic Rings. Journal of Neutrosophic and Fuzzy Systems. (): 55-60. DOI: https://doi.org/10.54216/JNFS.010201
    D., K. Bal, M. Aswad, M. "A Short Note On The Solutions Of Fermat's Diohantine Equation In Some Neutrosophic Rings," Journal of Neutrosophic and Fuzzy Systems, vol. , no. , pp. 55-60, 2021. DOI: https://doi.org/10.54216/JNFS.010201