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On the diophantine equation F<sub>n</sub> + F<sub>m</sub> = 2<sup>a</sup>
Abstract
In this paper, we find all the solutions of the title Diophantine equation in positive integer variables (n, m, a), where Fk is the kth term of the Fibonacci sequence. The proof of our main theorem uses lower bounds for linear forms in logarithms (Baker's theory) and a version of the Baker-Davenport reduction method in diophantine approximation.
Keywords: Fibonacci numbers, Zeckendorf representation, linear forms in logarithms, reduction method
