AbstractIn 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.Mathematics Subject Classification (2010): 11B3911J8611D61Key words: Fibonacci numbersZeckendorf representationlinear forms in logarithmsreduction method