Results 11 to 20 of about 312 (173)
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
doaj +2 more sources
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
openaire +3 more sources
Max–min of polynomials and exponential diophantine equations [PDF]
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
openaire +3 more sources
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
core +1 more source
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
core +1 more source
Linear forms in logarithms and exponential Diophantine equations [PDF]
, 2020 This paper aims to show two things. Firstly the importance of Alan Baker's work on linear forms in logarithms for the development of the theory of exponential Diophantine equations.
Rob Tijdeman, Tijdeman, Rob
core +1 more source
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 ...
openaire +1 more source
Two exponential diophantine equations [PDF]
Journal de théorie des nombres de Bordeaux, 2017 The equation 3 a + 5 b -
openaire +1 more source
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.
core +4 more sources
A NOTE ON EXPONENTIAL DIVISORS AND RELATED ARITHMETIC FUNCTIONS [PDF]
, 2006 Let n > 1 be a positive ...
Sandor, J.
core +1 more source