Abstract
In this paper, we find all sums of two Fibonacci numbers which are close to a power of 2. As a corollary, we also determine all Lucas numbers close to a power of 2. The main tools used in this work are lower bounds for linear forms in logarithms due to Matveev and Dujella–Pethö version of the Baker–Davenport reduction method in diophantine approximation. This paper continues and extends the previous work of Chern and Cui.
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Acknowledgements
The author would like to thank Professor Florian Luca for his constructive comments which helped to improve the presentation of this paper. He is also grateful to the anonymous referee for his/her valuable comments.
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This research was supported by NSERC Discovery grants RGPIN-2020-06731 of Habiba Kadiri and RGPIN-2020-06032 of Nathan Ng.
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Hasanalizade, E. Sums of Fibonacci numbers close to a power of 2. Bol. Soc. Mat. Mex. 29, 19 (2023). https://doi.org/10.1007/s40590-023-00490-7
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DOI: https://doi.org/10.1007/s40590-023-00490-7