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Cubic Diophantine Inequalities
Acta Mathematica Sinica, English Series, 2001In 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, 2008zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Delgado, M. +3 more
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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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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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Two Diophantine Inequalities over Primes with Fractional Power
Frontiers of Mathematics, 2023Huafeng Liu
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Diophantine inequalities over Piatetski-Shapiro primes
Frontiers of Mathematics in China, 2021Jing Huang, W. Zhai, D. Zhang
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The Solubility of Certain Diophantine Inequalities
Proceedings of the London Mathematical Society, 1958The 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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On a Diophantine Inequality with Reciprocals
Proceedings of the Steklov Institute of Mathematics, 2017zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Diophantine Inequalities for Forms
1991A form F(λ) of degree k can be written as $$ F\left( \lambda \right) = \mathop{\sum }\limits_{{1 \leqslant {{i}_{1}}, \ldots ,{{i}_{k}} \leqslant s}} a\left( {{{i}_{1}}, \ldots ,{{i}_{k}}} \right){{\lambda }_{{{{i}_{l}}}}} \cdots {{\lambda }_{{{{i}_{k}}}}} $$ we associate the multilinear form $$ \hat F\left( \lambda \right) = \sum\limits_{1 \
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On Some Nonlinear Diophantine Inequalities with Primes
Mathematical Notes, 2019A. Naumenko
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Systems of cubic Diophantine inequalities
Journal für die reine und angewandte Mathematik (Crelles Journal), 2004The main purpose of this work is to show that whenever \(R\) and \(s\) are positive integers with \(s\geq(10R)^{(10R)^5}\), then for any given real cubic forms \(C_1({\mathbf x}), \ldots, C_R({\mathbf x})\) in \(s\) variables, there exists a vector \({\mathbf x}=(x_1,\ldots,x_s)\) with integers \(x_1,\ldots,x_s\), not all zero, satisfying \(| C_i ...
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