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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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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 $$(m^2+m+1)^x+m^y=(m+1)^z $$
Mediterranean Journal of Mathematics, 2020Murat Alan
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A NOTE ON THE TERNARY PURELY EXPONENTIAL DIOPHANTINE EQUATION fx+(f+g)y=gz
Tsukuba Journal of Mathematics, 2023Y. Fujita, Maohua Le, N. Terai
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The Decision Problem for Exponential Diophantine Equations
The Annals of Mathematics, 1961Davis, Martin +2 more
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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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An Exponential Diophantine Equation with Generalized Pell Numbers
Bulletin of the Brazilian Mathematical Society, New SeriesJhon J. Bravo +2 more
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