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Proceedings - Mathematical Sciences

, Volume 127, Issue 3, pp 411–421 | Cite as

On a problem of Pillai with Fibonacci numbers and powers of 2

  • MAHADI DDAMULIRAEmail author
  • FLORIAN LUCA
  • MIHAJA RAKOTOMALALA
Article

Abstract

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.

Keywords

Fibonacci numbers linear forms in logarithms reduction method. 

2000 Mathematics Subject Classification.

11B39, 11J86. 

Notes

Acknowledgements

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.

References

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Copyright information

© Indian Academy of Sciences 2017

Authors and Affiliations

  • MAHADI DDAMULIRA
    • 1
    Email author
  • FLORIAN LUCA
    • 2
  • MIHAJA RAKOTOMALALA
    • 3
  1. 1.Institute of Analysis and Number TheoryGraz University of TechnologySteyrergasse 30/IIAustria
  2. 2.School of MathematicsUniversity of the WitwatersrandJohannesburgSouth Africa
  3. 3.AIMS Ghana (Biriwa)Cape CoastGhana

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