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On Pythagoras Triples in Symbolic 3-Plithogenic Rings [PDF]
Neutrosophic Sets and Systems, 2023 The objective of this paper is to find necessary and sufficient conditions for a symbolic 3-plithogenic triple (๐ก0 + ๐ก1๐1 + ๐ก2๐2 + ๐ก3๐3, ๐ 0 + ๐ 1๐1 + ๐ 2๐2 + ๐ 3๐3, ๐0 + ๐1๐1 + ๐2๐2 + ๐3๐3 ) to be a Pythagoras triple, i.e.
Abuobida Mohammed A. Alfahal +3 more
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Application of the group action approach to solving linear Diophantine equations [PDF]
ะะทะฒะตััะธั ะกะฐัะฐัะพะฒัะบะพะณะพ ัะฝะธะฒะตััะธัะตัะฐ. ะะพะฒะฐั ัะตัะธั: ะะฐัะตะผะฐัะธะบะฐ. ะะตั
ะฐะฝะธะบะฐ. ะะฝัะพัะผะฐัะธะบะฐThe article substantiates a method for solving linear Diophantine equations using the theory of group actions. The purpose of this paper is to introduce actions of certain groups on the set of linear Diophantine equations and to study their ...
Chistov, Ivan Sergeevich +1 more
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The Frobenius Number for Jacobsthal Triples Associated with Number of Solutions
Axioms, 2023 In this paper, we find a formula for the largest integer (p-Frobenius number) such that a linear equation of non-negative integer coefficients composed of a Jacobsthal triplet has at most p representations.
Takao Komatsu, Claudio Pita-Ruiz
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Small solutions of linear Diophantine equations
Discrete Mathematics, 1986 Given a system of linear diophantine equations and let (*) \(Ax=B\) be its matrix form, where \(A=(a_{ij})\) is a \(m\times n\), \(x=(x_k)\) and \(B=(a_{k,n+1})\) are \(m\times 1\) matrices. Further, given integers \(1\leq j_1< \cdots < j_m\leq n+1\), let \(d_{j_1,\ldots, j_m} = \det (a_{i,j_r}),\) \(1\leq i,r\leq m\), \(X=\sup \{| d_{j_1,\ldots, j_m}|:
I. Borosh, M. Flahive, B. Treybig
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On the Conditions for Symbolic 3-Plithogenic Pythagoras Quadruples [PDF]
Neutrosophic Sets and Systems, 2023 The objective of this paper is to find the necessary and sufficient conditions for a symbolic 3-plithogenic quadruple (๐ก0 + ๐ก1๐1 + ๐ก2๐2 + ๐ก3๐3, ๐ 0 + ๐ 1๐1 + ๐ 2๐2 + ๐ 3๐3, ๐0 + ๐1๐1 + ๐2๐2 + ๐3๐3, ๐0 + ๐1๐1 + ๐2๐2 + ๐3๐3 ) to be a Pythagoras quadruple, i.e.
Abuobida Mohammed A. Alfahal +3 more
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Three Diophantine equations concerning the polygonal numbers [PDF]
Notes on Number Theory and Discrete MathematicsMany authors investigated the problem about the linear combination of two polygonal numbers being a perfect square, i.e., the Diophantine equation mPโ(x)+nPโ(y)=zยฒ, where Pโ(x) denotes the x-th k-polygonal number and m, n are positive integers.
Yong Zhang, Mei Jiang, Qiongzhi Tang
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Cryptography Using Linear Diophantine Equation
, 2022 : This study is focused on the encrypting and decrypting of messages using the Linear Diophantine Equation: where , that is the integers and are relatively prime.
Mark Kenneth C. Engcot
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Penerapan Kombinatorik pada Persamaan Diophantine Linier [PDF]
, 2022 In this paper we apply combinatoric principle on linear diophantine equation. The method being used on this research is theoritic method. Generally, the linear diophantine equation is a polynomial equation. The form of equation being solved in this paper
Aโlailliyyin1, Aโlailliyyin +2 more
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Geometry of the Minimal Solutions of a Linear Diophantine Equation [PDF]
SIAM Journal on Discrete Mathematics, 2021 Let $a_1,\ldots,a_n$ and $b_1,\ldots,b_m$ be fixed positive integers, and let ${\mathcal S}$ denote the set of all nonnegative integer solutions of the equation $x_1a_1+\cdots +x_na_n=y_1b_1+\cdots +y_mb_m$. A solution $(x_1,\ldots,x_n,y_1,\ldots,y_m)$ in ${\mathcal S}$ is called minimal if it cannot be expressed as the sum of two nonzero solutions in $
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Diophantine Equation in Logarithms [PDF]
, 2023 The main work of these pages is written by myself under the supervisor of Dr. Omar Kihel, pertaining to continued fractions and applications , linear form in logarithms and the solutions of Diophantine equation Fn1 + Fn2 + Fn3 + Fn4 = 6a .
Tian, Zhao
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