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Some conjectures in the theory of exponential Diophantine equations
Publicationes Mathematicae Debrecen, 2000The author formulates a conjecture which implies Pillai's conjecture and a theorem of \textit{A. Schinzel} and \textit{R. Tijdeman} [Acta Arith. 31, 199-264 (1976; Zbl 0339.10018)] that for a polynomial with integer coefficients and at least two distinct roots, there are only finitely many perfect powers in its values at integral points.
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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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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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ON EXPONENTIAL DIOPHANTINE EQUATIONS CONTAINING THE EULER QUOTIENT
Bulletin of the Australian Mathematical Society, 2014AbstractLet $a$ and $m$ be relatively prime positive integers with $a>1$ and $m>2$. Let ${\it\phi}(m)$ be Euler’s totient function. The quotient $E_{m}(a)=(a^{{\it\phi}(m)}-1)/m$ is called the Euler quotient of $m$ with base $a$. By Euler’s theorem, $E_{m}(a)$ is an integer.
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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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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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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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A NOTE ON THE TERNARY PURELY EXPONENTIAL DIOPHANTINE EQUATION fx+(f+g)y=gz
Tsukuba Journal of Mathematics, 2023Yasutsugu Fujita +2 more
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