Results 11 to 20 of about 618,965 (192)
Cubic Diophantine inequalities [PDF]
Mathematika, 1995 \textit{H. Davenport} and \textit{K. F. Roth} [Mathematika, 2, 81--96 (1955; Zbl 0066.29301)] showed that for \(s \geq 8\) the values of the real additive form \(\lambda_1 x^3_1 + \ldots + \lambda_s x^3_s\) on \(\mathbb{Z}^s\) are dense on the real line, provided that \(\lambda_1/ \lambda_2\) is irrational.
Roger C. Baker +2 more
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Old and new conjectured diophantine inequalities [PDF]
Bulletin of the American Mathematical Society, 1990 The original meaning of diophantine problems is to find all solutions of equations in integers or rational numbers, and to give a bound for these solutions.
S. Lang
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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.
J. C. Rosales
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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,
Donald E. Freeman
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Systems of quadratic diophantine inequalities [PDF]
Journal de théorie des nombres de Bordeaux, 2008 Let Q 1 ,⋯,Q r be quadratic forms with real coefficients. We prove that for any ϵ>0 the system of inequalities |Q 1 (x)|<ϵ,⋯,|Q r (x)|<ϵ has a nonzero integer solution, provided that the system Q 1 (x)=0,⋯,Q r (x)=0 has a nonsingular real solution and all forms in the real pencil generated by Q 1 ,⋯,Q r are irrational and have rank >8r.
Wolfgang Müller
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Mersenne version of Brocard-Ramanujan equation
Journal of New Results in Science, 2023 In this study, we deal with a special form of the Brocard-Ramanujan equation, which is one of the interesting and still open problems of Diophantine analysis.
Ayşe Nalli, Seyran İbrahimov
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Diophantine approximation with one prime, two squares of primes and one kth power of a prime
Open Mathematics, 2021 Let ...
Gambini Alessandro
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Diophantine Inequalities for Generic Ternary Diagonal Forms [PDF]
International mathematics research notices, 2018 Let $k\geq 2$ and consider the Diophantine inequality $$ \left|x_1^k-{\alpha}_2 x_2^k-{\alpha}_3 x_3^k\right|
D. Schindler
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Diophantine approximations with a constant right-hand side of inequalities on short intervals. 1
Doklady of the National Academy of Sciences of Belarus, 2021 The problem of finding the Lebesgue measure 𝛍 of the set B1 of the coverings of the solutions of the inequality, ⎸Px⎹ n , Q ∈ N and Q >1, in integer polynomials P (x) of degree, which doesn’t exceed n and the height H (P) ≤ Q , is one of the main ...
V. Bernik, N. Budarina, E. V. Zasimovich
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Diophantine approximation with the constant right-hand side of inequalities on short intervals
Doklady of the National Academy of Sciences of Belarus, 2021 In the metric theory of Diophantine approximations, one of the main problems leading to exact characteristics in the classifications of Mahler and Koksma is to estimate the Lebesgue measure of the points x ∈ B ⊂ I from the interval I such as the ...
V. Bernik, D. Vasilyev, E. V. Zasimovich
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