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

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 , 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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