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On a general Diophantine inequality
Functiones Et Approximatio, Commentarii Mathematici, 2017 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Min Ru
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On a Diophantine Inequality Over Primes (II)
Monatshefte Fur Mathematik, 2006Suppose that \(c > 1\) is not an integer. Let \(H(c)\) denote the least integer \(r\) such that for any fixed \(\varepsilon > 0\) and for any \(N > N_0(c, \varepsilon) > 0\), the inequality \[ \left| p_1^c + p_2^c + \dots + p_r^c - N \right| < \varepsilon \] has solutions in prime numbers \(p_1, p_2, \dots, p_r\).
Wenguang Zhai
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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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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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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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On two Diophantine inequalities over primes [PDF]
Indagationes Mathematicae, 2018 21 ...
Min Zhang, Jinjiang Li
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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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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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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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