Sums of Fibonacci numbers that are perfect powers
Year: 2022
Type: article
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.
Source: Quaestiones Mathematicae
Author: Volker Ziegler
Institution: University of Salzburg
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
Funder: Austrian Science Fund
OpenAlex ID: W3146069697