Abstract
We consider the exponential Diophantine equation $a^{x}+b^{y}=c^{z}$ in positive integers $x$, $y$ and $z$, where $a$, $b$ and $c$ are fixed pair-wise relatively prime positive integers greater than one. In this paper, we obtain several upper bounds for solutions $x$, $y$ and $z$ for which two of $x$, $y$ and $z$ are even. As their applications, we solve exponential Diophantine equations in which $a$, $b$ and $c$ are expressed as terms of linearly recurrence sequences.
Citation
Takafumi Miyazaki. "Upper bounds for solutions of an exponential Diophantine equation." Rocky Mountain J. Math. 45 (1) 303 - 344, 2015. https://doi.org/10.1216/RMJ-2015-45-1-303
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