Results 111 to 120 of about 175 (143)
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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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Proportionally modular diophantine inequalities and their multiplicity
Acta Mathematica Sinica, English Series, 2010A proportionally modular Diophantine inequality has the form \(ax \, \text{mod} \, b \leq cx\), where \(a,b,c\) are positive integers. The set of integer solutions is a numerical semigroup: a subset of the natural numbers which contains zero, is closed under addition, and has finite complement. The authors present properties of such semigroups.
Rosales, J.C., Branco, M.B., Vasco, P
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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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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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Dual Diophantine Systems of Linear Inequalities
Journal of Mathematical Sciences, 2020zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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On a ternary Diophantine inequality
The Ramanujan Journal, 2016zbMATH 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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Asymptotic lower bounds for Diophantine inequalities
Mathematika, 2000Let \(F({\mathbf x})=\lambda_1 x_1^k+ \cdots +\lambda_s x_s^k\) be a diagonal form with non-zero real coefficients, whose ratios are not all rational, and such that, if \(k\) is even, then not all coefficients have the same sign. In this paper the author proves that there is an absolute real positive constant \(C\), such that for every \(\epsilon >0 ...
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Diophantine inequality by unlike powers of primes
The Ramanujan Journal, 2019zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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