The mathematical analysis of Linear Diophantine equations with two and three variables and Its Applications [PDF]
The Egyptian International Journal of Engineering Sciences and Technology, 2023 Linear Diophantine equation are introduced to determine and search for integral solutions according to the associated variables. In this paper, the mathematical techniques are approached to solve Linear Diophantine equation with two, three unknowns and ...
Rania Amer
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An Introduction to Refined Neutrosophic Number Theory [PDF]
Neutrosophic Sets and Systems, 2021 Number theory is concerned with properties of integers and Diophantine equations. The objective of this paper is dedicated to introduce the basic concepts in refined neutrosophic number theory such as division, divisors, congruencies, and Pell's equation
Mohammad Abobala, Muritala Ibrahim
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Neutrosophic Linear Diophantine Equations with Two Variables [PDF]
Neutrosophic Sets and Systems, 2020 This paper studies for the first time the neutrosophic linear Diophantine equations with two variables in the neutrosophic ring of integers, and refined neutrosophic ring of integers.
Hasan Sankari, Mohammad Abobala
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Lucas sequences and repdigits [PDF]
Mathematica Bohemica, 2022 Let $(G_n)_{n \geq1}$ be a binary linear recurrence sequence that is represented by the Lucas sequences of the first and second kind, which are $\{U_n\}$ and $\{V_n\}$, respectively.
Hayder Raheem Hashim, Szabolcs Tengely
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A Study of Symbolic 2-Plithogenic Split-Complex Linear Diophantine Equations in Two Variables [PDF]
Neutrosophic Sets and Systems, 2023 The equation 𝐴𝑋 + 𝐵𝑌 = 𝐶 is called symbolic 2-plithogenic linear Diophantine equation with two variables if 𝐴, 𝐵, 𝑋, 𝑌, 𝐶 are symbolic 2-plithogenic split-complex integers.
Rama Asad Nadweh +3 more
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A New Algorithm Based on Colouring Arguments for Identifying Impossible Polyomino Tiling Problems
Algorithms, 2022 Checkerboard colouring arguments for proving that a given collection of polyominoes cannot tile a finite target region of the plane are well-known and typically applied on a case-by-case basis. In this article, we give a systematic mathematical treatment
Marcus R. Garvie, John Burkardt
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On Some Algorithms for Solving Different Types of Symbolic 2-Plithogenic Algebraic Equations [PDF]
Neutrosophic Sets and Systems, 2023 The main goal of this paper is to study three different types of algebraic symbolic 2-plithogenic equations. The symbolic 2-plithogenic linear Diophantine equations, symbolic 2-plithogenic quadratic equations, and linear system of symbolic 2-plithgenic ...
Ahmad Khaldi +4 more
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Matrix Diophantine equations over quadratic rings and their solutions
Karpatsʹkì Matematičnì Publìkacìï, 2020 The method for solving the matrix Diophantine equations over quadratic rings is developed. On the basic of the standard form of matrices over quadratic rings with respect to $(z,k)$-equivalence previously established by the authors, the matrix ...
N.B. Ladzoryshyn +2 more
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On perfect powers in $k$-generalized Pell sequence [PDF]
Mathematica Bohemica, 2023 Let $k\geq2$ and let $(P_n^{(k)})_{n\geq2-k}$ be the $k$-generalized Pell sequence defined by \begin{equation*} P_n^{(k)}=2P_{n-1}^{(k)}+P_{n-2}^{(k)}+\cdots+P_{n-k}^{(k)} \end{equation*}for $n\geq2$ with initial conditions \begin{equation*} P_{-(k-2)}^{(
Zafer Şiar +2 more
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Generating Pythagoras Quadruples in Symbolic 2-Plithogenic Commutative Rings [PDF]
Neutrosophic Sets and Systems, 2023 This paper is dedicated to find a general algorithm for generating different solutions for Pythagoras non-linear Diophantine equation .
Yaser Ahmad Alhasan +2 more
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