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Quasi-polynomials, linear Diophantine equations and semi-linear sets [PDF]
Theoretical Computer Science, 2012 We investigate the family of semi-linear sets of N-t and Z(t). We study the growth function of semi-linear sets and we prove that such a function is a piecewise quasi-polynomial on a polyhedral partition of N-t.
Flavio D'Alessandro +2 more
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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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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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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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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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A Diophantine Equation Concerning Linear Recurrences
Periodica Mathematica Hungarica, 1997Let \(G_n ^{(1)}, \ldots, G_n ^{(\nu)}\) and \(H_n^{(1)}, \ldots, H_n ^{(\mu)}\) \((n=0, 1, 2,\ldots)\) be linear recurrence sequences of rational integers with order at least two. For fixed primes \(p_1 , \ldots , p_t \), let \(S\) be the set of integers of the form \(\pm p_1 ^{e_1 } \cdots p_t ^{e_t }\) \((e_i \geq 0)\). The author proves, under some
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2015
“I had a very strange dream last night,” Tweedledum said to Tweedledee. “I dreamt that we were not twins but quintuplets.” “What were the names of the others?” asked Tweedledee. “One of them was called Tweedledoo. I don't remember the other two, but they were also Tweedle-something. We had done something that was only possible in a dream. We made the
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“I had a very strange dream last night,” Tweedledum said to Tweedledee. “I dreamt that we were not twins but quintuplets.” “What were the names of the others?” asked Tweedledee. “One of them was called Tweedledoo. I don't remember the other two, but they were also Tweedle-something. We had done something that was only possible in a dream. We made the
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A Note on the Linear Diophantine Equation
The American Mathematical Monthly, 1941(1941). A Note on the Linear Diophantine Equation. The American Mathematical Monthly: Vol. 48, No. 10, pp. 662-666.
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