Results 11 to 20 of about 4,224,396 (192)
On Linear Diophantine Equation [PDF]
, 2017 {"references": ["1.\tDickson. L. E, History of the Theory of Numbers, Vol.2, Chelsea, New York, 1952. 2.\tKirch. A. M, Elementary Number Theory, In tent Educational \tpublisher, New York, 1974. 3.\tNagell. T, Introduction to Number Theory, Stockholm and New York, 1951. 4.\tOre. O, Number Theory and its History, McGraw \u2013 Hill. New York. 1948. 5.\
Dr. D. Ramprasad
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On the Number of Nonnegative Solutions to the Inequality a1 +....ar < n [PDF]
, 2010 In this paper, we present a simple and fast method for counting the number of nonnegative integer solutions to the equality a1x1+a2x2+: : :+arxr = n where a1; a2; :::; ar and n are positive integers.
Farzaneh , A. +3 more
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Solving Linear Diophantine Equations And Linear Congruential Equations
, 2012 This report represents GCD, euclidean algorithm, linear diophantine equation and linear congruential equation. It investigates the methods for solving linear diophantine equations and linear congruential equations in several variables. There are many examples which illustrate the methods for solving equations.
Yesilyurt, Deniz
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Tailoring Symmetry Breaking in Engineered van der Waals Superlattices. [PDF]
Adv MaterWe pioneer a scheme to tailor superpotentials in graphene based on intrinsic substrate electronic orders rather than twist angle. The resulting superpotential folds graphene's Dirac cones to either Γ$\Gamma$ or K‐points, leading to distinct symmetry behaviors.
Jin K +7 more
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Sparse Solutions of Linear Diophantine Equations [PDF]
SIAM Journal on Applied Algebra and Geometry, 2017 We present structural results on solutions to the Diophantine system $Ay = b$, $ y \in \mathbb{Z}^t_{\ge 0}$ that have the smallest number of nonzero entries. Our tools are algebraic and number theoretic in nature and include Siegel's lemma, generating functions, and commutative algebra.
Iskander Aliev +3 more
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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 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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On the Symbolic 2-plithogenic Fermat's Non-Linear Diophantine Equation [PDF]
Neutrosophic Sets and Systems, 2023 This paper is dedicated to find all symbolic 2-plithogenic integer solutions for the symbolic 2-plithogenic Fermat's Diophantine equation.
Heba Alrawashdeh +2 more
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The Computing of Pythagoras Triples in Symbolic 2-Plithogenic Rings [PDF]
Neutrosophic Sets and Systems, 2023 This paper is dedicated to finding a general algorithm for generating different solutions for Pythagoras' non-linear Diophantine equation in four variables 𝑥 2 + 𝑦 2 = 𝑧 2 in symbolic 2-plithogenic rings, which are known as Pythagoras triples.
Abuobida Mohammed A. Alfahal +3 more
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