Results 21 to 30 of about 580,253 (234)
Linear Diophantine equations in several variables [PDF]
Linear Algebra and its Applications, 2022 Let $R$ be a ring and let $(a_1,\dots,a_n)\in R^n$ be a unimodular vector, where $n\geq 2$ and each $a_i$ is in the center of $R$. Consider the linear equation $a_1X_1+\cdots+a_nX_n=0$, with solution set $S$. Then $S=S_1+\cdots+S_n$, where each $S_i$ is naturally derived from $(a_1,\dots,a_n)$, and we give a presentation of $S$ in terms of generators ...
Quinlan, R., Shau, M., Szechtman, F.
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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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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 Fast Method for Finding the Basis of Nonnegative Solutions to a Linear Diophantine Equation [PDF]
Journal of symbolic computation, 1995 We present a complete characterization of the set of minimal solutions of a single linear Diophantine equation in three unknowns over the natural numbers.
Miguel Filgueiras, Ana Paula Tomás
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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 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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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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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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On Some Methods for Solution of Linear Diophantine Equations
Universal Journal of Mathematics and Applications, 2020 The paper considers a linear Diophantine equation. A method (algorithm) for finding a general class of solutions of equation is proposed. The proposed algorithm is explained by examples of equations with two and three variables, trying to direct the ...
Azam Imomov, Yorqin T. Khodjaev
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Linear systems of Diophantine equations
The Electronic Journal of Linear Algebra, 2022 Given free modules $M\subseteq L$ of finite rank $f\geq 1$ over a principal ideal domain $R$, we give a procedure to construct a basis of $L$ from a basis of $M$ assuming the invariant factors or elementary divisors of $L/M$ are known. Given a matrix $A\in M_{m,n}(R)$ of rank $r$, its nullspace $L$ in $R^n$ is a free $R$-module of rank $f=n-r$.
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