Results 11 to 20 of about 175 (143)

Is there a computable upper bound for the height of a solution of a Diophantine equation with a unique solution in positive integers?

Open Computer Science, 2017
Let Bn = {xi · xj = xk : i, j, k ∈ {1, . . . , n}} ∪ {xi + 1 = xk : i, k ∈ {1, . . . , n}} denote the system of equations in the variables x1, . . . , xn. For a positive integer n, let _(n) denote the smallest positive integer b such that for each system
Tyszka Apoloniusz
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An improved estimate for certain Diophantine inequalities [PDF]

Proceedings of the American Mathematical Society, 1980
Let λ 1
Liu, M.C., Ng, Shu Ming, Tsang, K.M.
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From a packing problem to quantitative recurrence in [0,1] and the Lagrange spectrum of interval exchanges

Discrete Analysis, 2017
From a packing problem to quantitative recurrence in [0,1] and the Lagrange spectrum of interval exchanges, Discrete Analysis 2017:10, 25 pp. A basic fact in the theory of Diophantine approximation is Dirichlet's theorem that for every real number ...
Michael Boshernitzan, Vincent Delecroix
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Systems of quadratic diophantine inequalities [PDF]

Journal de théorie des nombres de Bordeaux, 2008
Let Q 1 , ⋯ , Q r
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Local Diophantine Nullstellen inequalities [PDF]

Journal of the American Mathematical Society, 1988
The main result of this paper is as follows. Let \(P_1,\ldots, P_n\) be polynomials of total degree at most \(D\) in \(x_1,\ldots,x_m\), with rational integer coefficients of absolute values at most \(H\).
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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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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 the Frobenius number of a modular Diophantine inequality [PDF]

Mathematica Bohemica, 2008
Summary: We present an algorithm for computing the greatest integer that is not a solution of the modular Diophantine inequality \(ax\bmod b\leq x\), with complexity similar to the complexity of the Euclid algorithm for computing the greatest common divisor of two integers.
Rosales, José Carlos, Vasco, Paulo
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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 ⁡
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A Diophantine Inequality Involving Mixed Powers of Primes with a Specific Type

Mathematics
Let λ1,λ2,λ3 be nonzero real numbers, not all of the same sign; let λ1/λ2 be irrational; and let η be any real number. We investigate the solvability of the inequality |λ1p1+λ2p2+λ3p32+η|0 in the prime variables p1, p2, and p3.
Tatiana L. Todorova, Atanaska Georgieva
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