On Pythagoras Triples in Symbolic 3-Plithogenic Rings

Abuobida Mohammed A. Alfahal; Yaser Ahmad Alhasan; Raja Abdullah Abdulfatah; Noor Edin Rabeh

doi:10.5281/zenodo.10031198

On Pythagoras Triples in Symbolic 3-Plithogenic Rings

Abuobida Mohammed A. Alfahal
, Yaser Ahmad Alhasan
, Raja Abdullah Abdulfatah
, Noor Edin Rabeh

Research output: Contribution to journal › Article › peer-review

Abstract

The objective of this paper is to find necessary and sufficient conditions for a symbolic 3-plithogenic triple (to + tiPi + t2P2 + t3P3,So + S1P1 + S2P2 + S3P3, ko + kiPi + k2?2 + k3P3~) to be a Pythagoras triple, i.e. to be a solution for the non-linear Diophantine equation X² + Y² = Z². Also, many examples will be illustrated and presented to explain how the theorems work.

Original language	English
Pages (from-to)	187-200
Number of pages	14
Journal	Neutrosophic Sets and Systems
Volume	59
DOIs	https://doi.org/10.5281/zenodo.10031198
State	Published - 2023
Externally published	Yes

Keywords

Pythagoras Diophantine equation
Pythagoras triple
symbolic 3-plithogenic ring

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10.5281/zenodo.10031198

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title = "On Pythagoras Triples in Symbolic 3-Plithogenic Rings",

abstract = "The objective of this paper is to find necessary and sufficient conditions for a symbolic 3-plithogenic triple (to + tiPi + t2P2 + t3P3,So + S1P1 + S2P2 + S3P3, ko + kiPi + k2?2 + k3P3\textasciitilde{}) to be a Pythagoras triple, i.e. to be a solution for the non-linear Diophantine equation X2 + Y2 = Z2. Also, many examples will be illustrated and presented to explain how the theorems work.",

keywords = "Pythagoras Diophantine equation, Pythagoras triple, symbolic 3-plithogenic ring",

author = "Alfahal, \{Abuobida Mohammed A.\} and Alhasan, \{Yaser Ahmad\} and Abdulfatah, \{Raja Abdullah\} and Rabeh, \{Noor Edin\}",

year = "2023",

doi = "10.5281/zenodo.10031198",

language = "English",

volume = "59",

pages = "187--200",

journal = "Neutrosophic Sets and Systems",

issn = "2331-6055",

publisher = "University of New Mexico",

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T1 - On Pythagoras Triples in Symbolic 3-Plithogenic Rings

AU - Alfahal, Abuobida Mohammed A.

AU - Alhasan, Yaser Ahmad

AU - Abdulfatah, Raja Abdullah

AU - Rabeh, Noor Edin

PY - 2023

Y1 - 2023

N2 - The objective of this paper is to find necessary and sufficient conditions for a symbolic 3-plithogenic triple (to + tiPi + t2P2 + t3P3,So + S1P1 + S2P2 + S3P3, ko + kiPi + k2?2 + k3P3~) to be a Pythagoras triple, i.e. to be a solution for the non-linear Diophantine equation X2 + Y2 = Z2. Also, many examples will be illustrated and presented to explain how the theorems work.

AB - The objective of this paper is to find necessary and sufficient conditions for a symbolic 3-plithogenic triple (to + tiPi + t2P2 + t3P3,So + S1P1 + S2P2 + S3P3, ko + kiPi + k2?2 + k3P3~) to be a Pythagoras triple, i.e. to be a solution for the non-linear Diophantine equation X2 + Y2 = Z2. Also, many examples will be illustrated and presented to explain how the theorems work.

KW - Pythagoras Diophantine equation

KW - Pythagoras triple

KW - symbolic 3-plithogenic ring

UR - https://www.scopus.com/pages/publications/85186540502

U2 - 10.5281/zenodo.10031198

DO - 10.5281/zenodo.10031198

M3 - Article

AN - SCOPUS:85186540502

SN - 2331-6055

VL - 59

SP - 187

EP - 200

JO - Neutrosophic Sets and Systems

JF - Neutrosophic Sets and Systems

ER -

On Pythagoras Triples in Symbolic 3-Plithogenic Rings

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Keywords

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