Results 11 to 20 of about 8,990 (153)
Proportionally modular diophantine inequalities
Journal of Number Theory, 2003 The authors study the sets of nonnegative solutions of Diophantine inequalities of the form \(ax\) mod \(b \leq cx\) with \(a, b\) and \(c\) positive integers. These sets are numerical semigroups, which are investigated and characterized.
Rosales, J.C. +3 more
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Quadratic Diophantine Inequalities
Journal of Number Theory, 2001 The theme of this paper is to investigate certain systems of Diophantine inequalities on real diagonal quadratic forms. First, let \(Q_1\) and \(Q_2\) be real diagonal quadratic forms in \(s\) variables, with \(s\geq 10\), and suppose that whenever \(\alpha\) and \(\beta\) are real numbers with \((\alpha,\beta)\neq(0,0)\), then the form \(\alpha Q_1 ...
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On two Diophantine inequalities over primes [PDF]
Indagationes Mathematicae, 2018 21 ...
Zhang, Min, Li, Jinjiang
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On pairs of cubic Diophantine inequalities
Mathematika, 1991 \textit{H. Davenport} and \textit{H. Heilbronn} [J. Lond. Math. Soc. 21, 185--193 (1946; Zbl 0060.11914)] proved that if \(Q({\mathbf x})=\sum^5_{j=1}\lambda_jx^2_j\) is an indefinite quadratic form with real coefficients \(\lambda_j\), such that at least one of the ratios \(\lambda_i/\lambda_j\) is irrational, then for any \(\varepsilon>0\) there ...
Brüdern, Jörg, Cook, R. J.
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Symmetric modular Diophantine inequalities [PDF]
Proceedings of the American Mathematical Society, 2006 In this paper we study and characterize those Diophantine inequalities a x mod b ≤ x ax\operatorname {mod} b\leq x whose set of solutions is a symmetric numerical semigroup.
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An exponential Diophantine equation related to the difference between powers of two consecutive Balancing numbers [PDF]
, 2018 In this paper, we find all solutions of the exponential Diophantine equation $B_{n+1}^x-B_n^x=B_m$ in positive integer variables $(m, n, x)$, where $B_k$ is the $k$-th term of the Balancing sequence.Comment: Comments are ...
Faye, Bernadette +3 more
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One Cubic Diophantine Inequality [PDF]
Journal of the London Mathematical Society, 2000 Let \(F(x)\) be a cubic form with real coefficients in \(s\) variables. \textit{J. Pitman} [J. Lond. Math. Soc. 43, 119-126 (1968; Zbl 0164.05301)] proved that there exists \(s_0> 0\) such that for any \(s\geq s_0\) the inequality \[ |F(x)|< 1 \tag{1} \] is solvable in \({\mathbf x}\in \mathbb{Z}^3\setminus \{\mathbf{0}\}\). About the quantitative part,
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On some diophantine inequalities involving primes.
Journal für die reine und angewandte Mathematik (Crelles Journal), 1967 openaire +4 more sources
Gowers norms control diophantine inequalities [PDF]
Algebra & Number Theory, 2017 A central tool in the study of systems of linear equations with integer coefficients is the Generalised von Neumann Theorem of Green and Tao. This theorem reduces the task of counting the weighted solutions of these equations to that of counting the weighted solutions for a particular family of forms, the Gowers norms $\Vert f \Vert_{U^{s+1}[N]}$ of ...
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Finiteness results for Diophantine triples with repdigit values [PDF]
, 2015 Let $g\ge 2$ be an integer and $\mathcal R_g\subset \mathbb N$ be the set of repdigits in base $g$. Let $\mathcal D_g$ be the set of Diophantine triples with values in $\mathcal R_g$; that is, $\mathcal D_g$ is the set of all triples $(a,b,c)\in \mathbb ...
Bérczes, Attila +3 more
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