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On Some Exponential Diophantine Equations [PDF]
Monatshefte Fur Mathematik, 2001 Let \(D_1,D_2\) be coprime positive integers, and let \(h\) denote the class number of the quadratic field \(\mathbb{Q} (\sqrt{-D_1D_2})\). In this paper, using a deep theorem concerning the existence of primitive divisors of Lucas and Lehmer numbers, the authors completely determine all solutions \((x,y,n)\) of the generalized Ramanujan-Nagell ...
Yann Bugeaud, Bugeaud Yann
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Exponential Diophantine Equations
Tutorials, Schools, and Workshops in the Mathematical Sciences, 2019This paper is a very gentle introduction to solving exponential Diophantine equations using the technology of linear forms in logarithms of algebraic numbers.
Florian Luca, Luca Florian
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The Undecidability of Exponential Diophantine Equations
Studies in Logic and the Foundations of Mathematics, 1966Publisher Summary This chapter focuses on the undecidability of exponential Diophantine equations. It is not known whether exponential Diophantine sets are necessarily Diophantine. However, it is known that every exponential Diophantine equation could be transformed mechanically into an equivalent ordinary Diophantine equation in more unknowns ...
Julia Robinson
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Conjunctions of exponential diophantine equations over $${\mathbb {Q}}$$
Archive for Mathematical LogiczbMATH Open Web Interface contents unavailable due to conflicting licenses.
Mihai Prunescu
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The Decision Problem for Exponential Diophantine Equations
Annals of Mathematics, 1961Julia Robinson
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ON THE SOLUTION OF A CLASS OF EXPONENTIAL DIOPHANTINE EQUATIONS
South East Asian J. of Mathematics and Mathematical Sciences, 2022In this note, we show that for n = 4N + 3, N N 0 , the expo- nential Diophantine equation nx + 24y = z2 has exactly two solutions if n + 1 or equivalently N + 1 is an square. When N + 1 = m2, the solutions are given by (0, 1, 5) and (1, 0, 2m). Otherwise it has a unique solution (0, 1, 5) in non-negative integers.
Dutta, Mridul, Borah, Padma Bhushan
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Annals of Mathematics, 2006 This is the first in a series of papers whereby we combine the classical approach to exponential Diophantine equations (linear forms in logarithms, Thue equations, etc.) with a modular approach based on some of the ideas of the proof of Fermat's Last ...
Yann Bugeaud +2 more
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