On a problem of Pillai with Fibonacci numbers and powers of 2
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In this paper, we find all integers c having at least two representations as a difference between a Fibonacci number and a power of 2.
KeywordsFibonacci numbers linear forms in logarithms reduction method.
2000 Mathematics Subject Classification.11B39, 11J86.
The authors would like to thank the referee for comments which improved the quality of this paper. They also thank J. J. Bravo for spotting a computational oversight in a previous version of this paper. The first author, MD was supported by the FWF Grant F5510 within the special research area (SFB) “Quasi Monte Carlo Methods: Theory and Applications” under the supervision of Prof. Dr. Robert F. Tichy.
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