315 304
Full Length Article
International Journal of Neutrosophic Science
Volume 22 , Issue 4, PP: 44-55 , 2023 | Cite this article as | XML | Html |PDF

Title

On Symbolic 7-Plithogenic and 8-Plithogenic Number Theoretical Concepts

  Luis Albarracín Zambrano 1 * ,   Fabricio Lozada Torres 2 ,   Bolívar Villalta Jadan 3 ,   Nabil Khuder Salman 4

1  Universidad Regional Autónoma de los Andes (UNIANDES), Ecuador
    (uq.luisalbarracin@uniandes.edu.ec)

2  Universidad Regional Autónoma de los Andes (UNIANDES), Ecuador
    (ua.fabriciolozada@uniandes.edu.ec)

3  Universidad Regional Autónoma de los Andes (UNIANDES), Ecuador
    (us.bolivarvillalta@uniandes.edu.ec)

4  College Of Pharmacy, AL-Farahidi University, Baghdad, Iraq
    (nsalman@uoalfarahidi.edu.iq)

Full Text Download


Doi   :   https://doi.org/10.54216/IJNS.220404

Received: June 13, 2023 Revised: August 04, 2023 Accepted: November 01, 2023

Abstract :

This paper is dedicated to studying the foundations of 7-plithogenic and 8-plithogenic number theory, where the central concepts about symbolic 7-plithogenic/8-plithogenic integers will be discussed such as symbolic 7-plithogenic/8-plithogenic Pythagoras triples and quadruples, symbolic 7-plithogenic/8-plithogenic linear Diophantine equations, and the divisors. On the other hand, we prove that Euler's theorem is still true in the case of the symbolic 7-plithogenic/8-pithogenic number theory.

Keywords :

symbolic 7-plithogenic integer; symbolic 7-plithogenic congruencies; symbolic 7-plithogenic phi-Euler's theorem; symbolic 8-plithogenic phi-Euler's theorem.

References :

[1] Nader Mahmoud Taffach , Ahmed Hatip., "A Review on Symbolic 2-Plithogenic Algebraic Structures " Galoitica Journal Of Mathematical Structures and Applications, Vol.5, 2023.

[2] Nader Mahmoud Taffach , Ahmed Hatip.," A Brief Review on The Symbolic 2-Plithogenic Number Theory and Algebraic Equations ", Galoitica Journal Of Mathematical Structures and Applications, Vol.5, 2023.

[3] Merkepci, H., and Abobala, M., " On The Symbolic 2-Plithogenic Rings", International Journal of Neutrosophic Science, 2023.

[4] Smarandache, F., " Introduction to the Symbolic Plithogenic Algebraic Structures (revisited)", Neutrosophic Sets and Systems, vol. 53, 2023.

[5] Taffach, N., " An Introduction to Symbolic 2-Plithogenic Vector Spaces Generated from The Fusion of Symbolic Plithogenic Sets and Vector Spaces", Neutrosophic Sets and Systems, Vol 54, 2023.

[6] Taffach, N., and Ben Othman, K., " An Introduction to Symbolic 2-Plithogenic Modules Over Symbolic 2-Plithogenic Rings", Neutrosophic Sets and Systems, Vol 54, 2023.

[7] Merkepci, H., and Rawashdeh, A., " On The Symbolic 2-Plithogenic Number Theory and Integers ", Neutrosophic Sets and Systems, Vol 54, 2023.

[8] Albasheer, O., Hajjari., A., and Dalla., R., " On The Symbolic 3-Plithogenic Rings and TheirAlgebraic Properties", Neutrosophic Sets and Systems, Vol 54, 2023.

[9] 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.

[10] 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.

[11] 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.

[12] 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.

[13] Ben Othman, K., Albasheer, O., Nadweh, R., Von Shtawzen, O., and Ali, R., "On The Symbolic 6-Plithogenic and 7-Plithogenic Rings", Galoitica Journal of Mathematical Structures and Applications, Vol.8, 2023.

[14] M. B. Zeina, N. Altounji, M. Abobala, and Y. Karmouta, “Introduction to Symbolic 2-Plithogenic Probability Theory,” Galoitica: Journal of Mathematical Structures and Applications, vol. 7, no. 1, 2023.

[15] Ali, R., and Hasan, Z., "An Introduction To The Symbolic 3-Plithogenic Vector Spaces", Galoitica Journal Of Mathematical Structures and Applications, vol. 6, 2023.

[16] Rawashdeh, A., "An Introduction To The Symbolic 3-plithogenic Number Theory", Neoma Journal Of Mathematics and Computer Science, 2023.

[17] Ben Othman, K., "On Some Algorithms For Solving Symbolic 3-Plithogenic Equations", Neoma Journal Of Mathematics and Computer Science, 2023.

[18] Florentin Smarandache: Plithogenic Set, an Extension of Crisp, Fuzzy, Intuitionistic Fuzzy, and Neutrosophic Sets – Revisited, Neutrosophic Sets and Systems, vol. 21, 2018, pp. 153-166.

[19] Abobala, M., Bal, M., Aswad, M., "A Short Note On Some Novel Applications of Semi Module Homomorphisms", International Journal of Neutrosophic Science, 2022.

[20] 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.

[21] Ben Othman, K., Von Shtawzen, O., Khaldi, A., and Ali, R., "On The Symbolic 8-Plithogenic Matrices", Pure Mathematics For Theoretical Computer Science, Vol.1, 2023.

[22] Soueycatt, M., Charchekhandra, B., Abu Hakmeh, R., " On The Algebraic Properties Of Symbolic 6-Plithogenic Integers", Neutrosophic Sets and Systems, vol. 59, 2023.

[23] Soueycatt, M., Charchekhandra, B., Abu Hakmeh, R., " On The Foundations Of Symbolic 5-Plithogenic Number Theory", Neutrosophic Sets and Systems, vol. 59, 2023.

[24] Abobala, M., " Partial Foundation of Neutrosophic Number Theory", Neutrosophic Sets and Systems, Vol. 39, 2021.

Cite this Article as :
Style #
MLA Luis Albarracín Zambrano, Fabricio Lozada Torres, Bolívar Villalta Jadan, Nabil Khuder Salman. "On Symbolic 7-Plithogenic and 8-Plithogenic Number Theoretical Concepts." International Journal of Neutrosophic Science, Vol. 22, No. 4, 2023 ,PP. 44-55 (Doi   :  https://doi.org/10.54216/IJNS.220404)
APA Luis Albarracín Zambrano, Fabricio Lozada Torres, Bolívar Villalta Jadan, Nabil Khuder Salman. (2023). On Symbolic 7-Plithogenic and 8-Plithogenic Number Theoretical Concepts. Journal of International Journal of Neutrosophic Science, 22 ( 4 ), 44-55 (Doi   :  https://doi.org/10.54216/IJNS.220404)
Chicago Luis Albarracín Zambrano, Fabricio Lozada Torres, Bolívar Villalta Jadan, Nabil Khuder Salman. "On Symbolic 7-Plithogenic and 8-Plithogenic Number Theoretical Concepts." Journal of International Journal of Neutrosophic Science, 22 no. 4 (2023): 44-55 (Doi   :  https://doi.org/10.54216/IJNS.220404)
Harvard Luis Albarracín Zambrano, Fabricio Lozada Torres, Bolívar Villalta Jadan, Nabil Khuder Salman. (2023). On Symbolic 7-Plithogenic and 8-Plithogenic Number Theoretical Concepts. Journal of International Journal of Neutrosophic Science, 22 ( 4 ), 44-55 (Doi   :  https://doi.org/10.54216/IJNS.220404)
Vancouver Luis Albarracín Zambrano, Fabricio Lozada Torres, Bolívar Villalta Jadan, Nabil Khuder Salman. On Symbolic 7-Plithogenic and 8-Plithogenic Number Theoretical Concepts. Journal of International Journal of Neutrosophic Science, (2023); 22 ( 4 ): 44-55 (Doi   :  https://doi.org/10.54216/IJNS.220404)
IEEE Luis Albarracín Zambrano, Fabricio Lozada Torres, Bolívar Villalta Jadan, Nabil Khuder Salman, On Symbolic 7-Plithogenic and 8-Plithogenic Number Theoretical Concepts, Journal of International Journal of Neutrosophic Science, Vol. 22 , No. 4 , (2023) : 44-55 (Doi   :  https://doi.org/10.54216/IJNS.220404)
↑