Results 121 to 130 of about 12,497 (156)

Diophantine inequality involving binary forms

Frontiers of Mathematics in China, 2013
This paper is concerned with the study of Diophantine inequalities that are composed of binary forms. Let \(\phi_j\in \mathbb{Z}[x,y]\) for \(1\leq j\leq s\) be nondegenerate homogeneous forms of degree \(d=3\) or \(d=4\). Assume that \(\lambda_i\) for \(1\leq i\leq s\) are non-zero real numbers such that \(\frac{\lambda_1}{\lambda_2}\) is irrational ...
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Cubic Diophantine Inequalities

Acta Mathematica Sinica, English Series, 2001
In this paper, it is proved that for any real numbers \(\lambda_1\), \(\lambda_2,\ldots,\lambda_7\) with \(\lambda_i\geq 1\) \((1\leq i\leq 7)\), the Diophantine inequality \[ |\lambda_1x_1^3+\lambda_2x_2^3+\cdots+\lambda_7x_7^3|
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Systems of proportionally modular Diophantine inequalities

Semigroup Forum, 2008
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Delgado, M.   +3 more
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Dual Diophantine Systems of Linear Inequalities

Journal of Mathematical Sciences, 2020
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Diophantine inequalities

1993
Abstract In order to proceed, it is necessary to show that the positive solution sets of systems of linear Diophantine equations are finitely generated. One might compare this with the famous simplex algorithm, which is well known to the practitioners of economic speculation.
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The Solubility of Certain Diophantine Inequalities

Proceedings of the London Mathematical Society, 1958
The author proves the following theorem: Let \(\lambda_1, \ldots, \lambda_{14}\) be non-zero real numbers, not all of the same sign, and suppose that \(\lambda_1/\lambda_2\) is irrational. Then, for any real \(\gamma\), and any \(\varepsilon > 0\), the inequality \[ \vert \lambda_1x_1^4 + \ldots + \lambda_{14}x_{14}^4 < \varepsilon \] has infinitely ...
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