Abstract
Let us denote by Fn the n-th Fibonacci number. In this paper we show that for a fixed integer y there exists at most one integer exponent a > 0 such that the Diophantine equation Fn + Fm = ya has a solution (n, m, a) in positive integers satisfying n > m > 0, unless y = 2, 3, 4, 6 or 10.
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