Research Article

On sums of two Fibonacci numbers that are powers of numbers with limited hamming weight

Published in: Quaestiones Mathematicae
Volume 47 , issue 4 : Entrepreneurship and Africa’s Cultural Context , 2024 , pages: 851–869
DOI: 10.2989/16073606.2023.2256477
Author(s): Ingrid Vukusic University of Salzburg, Austria, Volker Ziegler University of Salzburg, Austria,
Keywords: 11B39, 11D61, 11J86, Fibonacci numbers, Zeckendorf representation, exponential Diophantine equation, linear forms in logarithms,
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Abstract

In 2018, Luca and Patel conjectured that the largest perfect power representable as the sum of two Fibonacci numbers is 38642 = F 36 + F 12. In other words, they conjectured that the equation
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