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On Aggregating Two Linear Diophantine Equations
Discrete Applied Mathematics, 1998 Given two diophantine equations \[ \sum_{j\in \mathbb{N}} a_{1j}x_j= b_1,\;\sum_{j\in \mathbb{N}}a_{2j}x_j= b_2, \quad x_j\geq 0\text{ for all }j\in \mathbb{N}= \{1,\dots, n\}, \tag{1} \] the problem is to find relatively prime integers \(t_1,t_2\), so that \[ \sum_{j\in \mathbb{N}} (t_1a_{1j}+ t_2a_{2j})x_j= t_1b_1+ t_2b_2 \tag{2} \] has the same ...
Kevin Broughan
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On a Linear Diophantine Equation
Proceedings of the Indian Academy of Sciences - Section A, 1940S S Pillai
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Linear Diophantine Equations and Local Cohomology
Inventiones Mathematicae, 1982 If \(\mathbb R\), \(\mathbb Q\), \(\mathbb Z\), \(\mathbb N\) and \(\mathbb P\) have the usual meanings and if \(\Phi\) is an \(r\times n\) matrix over \(\mathbb Z\), then \(E = E^0\), where \(E^\alpha = \{\beta\in\mathbb N^n\mid \Phi\beta = \alpha\).
Richard P Stanley
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1995
A linear Diophantine equation in two variables is an equation of the form ax + by = c where a, b and c are given integers, and x and y are unknown integers. Sometimes x and y are restricted to the set of positive integers.
W. S. Anglin, J. Lambek
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A linear Diophantine equation in two variables is an equation of the form ax + by = c where a, b and c are given integers, and x and y are unknown integers. Sometimes x and y are restricted to the set of positive integers.
W. S. Anglin, J. Lambek
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2020
A study of linear Diophantine equations, with a focus on the Frobenius number and the denumerants.
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A study of linear Diophantine equations, with a focus on the Frobenius number and the denumerants.
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On solving probabilistic linear Diophantine equations
J. Mach. Learn. Res., 2021Summary: Multiple methods exist for computing marginals involving a linear Diophantine constraint on random variables. Each of these extant methods has some limitation on the dimension and support or on the type of marginal computed (e.g., sum-product inference, max-product inference, maximum a posteriori, etc.).
Patrick Kreitzberg, Oliver Serang
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Solving Linear Diophantine Equations
2023Linear diophantine equations are at the heart of any unification algorithm for associative and commutative theories. The known algorithms for solving homogeneous linear diophantine equations of Huet and Fortenbacher are presented and their implementation is compared. The algorithms for homogeneous equations are extended to solve inhomogeneous equations,
Guckenbiehl, Thomas, Herold, Alexander
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Mathematics Magazine, 1958
We shall describe elementary methods for solving linear Diophantine equations, either single equations or systems of equations. The equations with which we shall deal have integral coefficients and require integral solutions. Such equations are named after Diophantus of Alexandria, who lived probably between 100 and 300 A. D.
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We shall describe elementary methods for solving linear Diophantine equations, either single equations or systems of equations. The equations with which we shall deal have integral coefficients and require integral solutions. Such equations are named after Diophantus of Alexandria, who lived probably between 100 and 300 A. D.
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The Linear Diophantine Equation
The American Mathematical Monthly, 1981(1981). The Linear Diophantine Equation. The American Mathematical Monthly: Vol. 88, No. 3, pp. 200-203.
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1988
A linear diophantine equation has the form $$ {a_1}{x_1} + {a_2}{x_2} + ... + {a_n}{x_n} = c $$ where a1, a2,..., an, c are integer constants and x1, x2,..., xn are integer variables. As we saw in Chapter 3, these equations play a very important role in the linear dependence problem.
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A linear diophantine equation has the form $$ {a_1}{x_1} + {a_2}{x_2} + ... + {a_n}{x_n} = c $$ where a1, a2,..., an, c are integer constants and x1, x2,..., xn are integer variables. As we saw in Chapter 3, these equations play a very important role in the linear dependence problem.
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