Results 11 to 20 of about 312 (174)
The Exponential Diophantine Equation 4m2+1x+5m2-1y=(3m)z [PDF]
Abstract and Applied Analysis, 2014 Let m be a positive integer. In this paper, using some properties of exponential diophantine equations and some results on the existence of primitive divisors of Lucas numbers, we prove that if m>90 and 3|m, then the equation 4m2+1x + 5m2-1y=(3m)z has ...
Juanli Su, Xiaoxue Li
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Small two-variable exponential Diophantine equations [PDF]
Mathematics of Computation, 1993 We examine exponential Diophantine equations of the form a b x = c d y + e a{b^x} = c{d^y} + e . Consider a ≤ 50 a \leq 50 , c ≤
Robert Styer
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Max–min of polynomials and exponential diophantine equations
Journal of Number Theory, 2010 In the first half of this paper, largely based on earlier work of \textit{R. Dvornicich, U. Zannier}, and the author [Acta Arith. 106, No. 2, 115--121 (2003; Zbl 1020.11018)], it is shown that for \(F \in {\mathbb Z}[x,y]\) one has \(\max_{x \in \mathbb Z \cap [-T,T]} \min_{y \in \mathbb Z} |F(x,y)| = o(T^{1/2})\) as \(T \to \infty\) if and only if ...
Tung, Shih Ping
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GEOMETRIC THEOREMS, DIOPHANTINE EQUATIONS, AND ARITHMETIC FUNCTIONS [PDF]
, 2002 This book contains short notes or articles, as well as studies on several topics of Geometry and Number theory. The material is divided into ve chapters: Geometric theorems; Diophantine equations; Arithmetic functions; Divisibility properties of numbers ...
Sándor, József
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Subconvexity for additive equations: Pairs of undenary cubic forms [PDF]
, 2014 We investigate pairs of diagonal cubic equations with integral coefficients. For a class of such Diophantine systems with 11 or more variables, we are able to establish that the number of integral solutions in a large box is at least as large as the ...
Brueden, Joerg +4 more
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Two exponential Diophantine equations [PDF]
Glasgow Mathematical Journal, 1997 In [3], two open problems were whether either of the diophantine equationswith n ∈ Z and f a prime number, is solvable if ω > 3 and 3 √ ω, but in this paper we allow f to be any (rational) integer and also 3 | ω. Equations of this form and more general ones can effectively be solved [5] with an advanced method based on analytical results, but the ...
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Two exponential diophantine equations [PDF]
Journal de théorie des nombres de Bordeaux, 2017 The equation 3 a + 5 b -
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Sub-exponential stability for the beam equation [PDF]
, 2023 We consider a one-parameter family of beam equations with Hamiltonian non-linearity in one space dimension under periodic boundary conditions. In a unified functional framework we study the long time evolution of initial data in two categories of ...
Feola R., Massetti J. E.
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A NOTE ON EXPONENTIAL DIVISORS AND RELATED ARITHMETIC FUNCTIONS [PDF]
, 2006 Let n > 1 be a positive ...
Sandor, J.
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Padovan and Perrin numbers of the form 7ᵗ-5ᶻ-3ʸ-2ˣ [PDF]
Notes on Number Theory and Discrete MathematicsConsider the Padovan sequence (pₙ)ₙ≥₀ given by pₙ₊₃=pₙ₊₁+pₙ with p₀=p₁=p₂=1. Its companion sequence, the Perrin sequence (℘ₙ)ₙ≥₀, follows the same recursive formula as the Padovan numbers, but with different initial values: p₀=3, p₁=0 and p₂=2.
Djamel Bellaouar +2 more
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