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Exponential Diophantine equations over function fields
Publicationes Mathematicae Debrecen, 1992Let \(k\) be an algebraically closed field of characteristic zero and let \(k(t)\) be the field of rational functions over \(k\). Further, let \(\mathbb{K}\) be a finite extension of \(k(t)\). For given non-zero elements \(f_ 1,\ldots,f_ n,g\) of \(\mathbb{K}[X_ 1,\ldots,X_ n]\) \((n\geq 2)\), consider the equation \[ \sum^ n_{i=1}f_ i({\mathbf x ...
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The Undecidability of Exponential Diophantine Equations
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 ...
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On the Exponential Diophantine Equation $F_{n+1}^x - F_{n-1}^x = F_m^y$
Taiwanese Journal of Mathematics, 2022Florian Luca
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The Decision Problem for Exponential Diophantine Equations
The Annals of Mathematics, 1961Davis, Martin +2 more
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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.
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On the Exponential Diophantine Equation $(a^n-1)(b^n-1)=x^2$
Bulletin of the Belgian Mathematical Society - Simon Stevin, 2020Alain Togbé
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On the Exponential Diophantine Equation $$ p^x+q^y=z^3: $$ Theorems and Conjectures
Advances in Intelligent Systems and Computing, 2022Jerico B Baćani, Ronald Lachica Aquino
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On the exponential Diophantine equation Pm2
This study investigates numbers that are powers of two and can be expressed as the sum of the squares of any two Pell numbers. We apply Baker's theory of linear forms in logarithms of algebraic numbers, along with a variation of the Baker-Davenport reduction method, to solve the Diophantine equation P-m(2) + P-n(2) = 2a, where m,n, and a are non ...Emin, Ahmet, Ates, Firat
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