Research Article

Sums of Fibonacci numbers that are perfect powers

Published in: Quaestiones Mathematicae
Volume 46 , issue 8 : Entrepreneurship and Africa’s Cultural Context , 2024 , pages: 1717–1742
DOI: 10.2989/16073606.2022.2109220
Author(s): Volker Ziegler University of Salzburg, Austria,
Keywords: 11D61, 11B39, 11D45, 11Y50, Baker’s method, Fibonacci numbers, Diophantine equations,
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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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