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.
We’re sorry, something doesn't seem to be working properly.
Please try refreshing the page. If that doesn't work, please contact support so we can address the problem.
References
Baker A and Davenport H, The equations 3x 2 − 2 = y 2 and 8x 2 − 7 = z 2, Quart. J Math. Ser. (2) 20 (1969) 129–137
Dujella A and Pethő A, A generalization of a theorem of Baker and Davenport, Quart. J. Math. Oxford Ser. (2) 49 (1998) 291–306
Herschfeld A, The equation 2x − 3y = d, Bull. Amer. Math. Soc. 41 (1935) 631
Herschfeld A, The equation 2x − 3y = d, Bull. Amer. Math. Soc. 42 (1936) 231–234
Matveev E M, An explicit lower bound for a homogeneous rational linear form in the logarithms of algebraic numbers II, Izv. Ross. Akad. Nauk Ser. Mat. 64 (2000) 125–180 ; translation in Izv. Math. 64 (2000) 1217–1269
Pillai S S, On a x − b y = c, J. Indian Math. Soc. (N.S.) 2 (1936) 119–122
Pillai S S, A correction to the paper, “On a x − b y = c”, J. Indian Math. Soc. 2 (1937) 215
Stroeker R J and Tijdeman R, Diophantine equations, in: Computational methods in number theory, Part II, vol. 155 of Math. Centre Tracts, Math. Centrum (1982) (Amsterdam) pp. 321–369
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.
Author information
Authors and Affiliations
Corresponding author
Additional information
Communicating Editor: B Sury
Rights and permissions
About this article
Cite this article
DDAMULIRA, M., LUCA, F. & RAKOTOMALALA, M. On a problem of Pillai with Fibonacci numbers and powers of 2. Proc Math Sci 127, 411–421 (2017). https://doi.org/10.1007/s12044-017-0338-3
Received:
Revised:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s12044-017-0338-3