On the Exponential Diophantine Equation (Fm+1(k))x-(Fm-1(k))x = Fn(k)
Abstract
In this paper, we explicitly find all solutions of the title Diophantine equation, using lower bounds for linear forms in logarithms and properties of continued fractions. Further, we use a version of the Baker-Davenport reduction method in Diophantine approximation, due to Dujella and Peth\"o. This paper extends the previous work of Patel.
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