Nurettin Irmak and Bo He

Notes on Number Theory and Discrete Mathematics

Print ISSN 1310–5132, Online ISSN 2367–8275

Volume 25, 2019, Number 4, Pages 102–109

DOI: 10.7546/nntdm.2019.25.4.102-109

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## Details

### Authors and affiliations

Nurettin Irmak

*Department of Mathematics, Art and Science Faculty,
Niğde Ömer Halisdemir University, Turkey
*

Bo He

*Institute of Mathematics, Aba Teachers University
Wenchuan, Sichuan, 623000 P. R. China
*

### Abstract

In this paper, we solve the Diophantine equation , where and are positive integers with

### Keywords

- Fibonacci numbers
- Linear forms in logarithms
- Reduction method
*s*-th power

### 2010 Mathematics Subject Classification

- 11B39
- 11J86

### References

- Bertók, C., Hajdu, L., Pink, I. & Rábai, Z. (2017). Linear combinations of prime powers in binary recurrence sequences. Int. J. Number Theory, 13 (2), 261–271.
- Bugeaud, Y., Mignotte, M., & Siksek, S. (2006). Classical and modular approaches to exponential Diophantine equation. I. Fibonacci and Lucas perfect powers. Ann of Math, 163, 969–1018.
- Bravo, J. J., & Luca, F. (2012). Powers of two in generalized Fibonacci sequence.Rev Colombiana Math, 46, 67–79.
- Luca, F. & Szalay, L. (2007). Fibonacci numbers of the form . The Fibonacci Quarterly, 45, 98–103.
- Marques, D. & Togbé, A. (2013). Fibonacci and Lucas numbers of the form Proc Japan Acad, 89, 47–50.
- Matveev, E. M. (2000). An explicit lower bound for a homogeneous linear form in logarithms of algebraic numbers. II, Izv Ross Akad Nauk Ser Mat, 64 (6), 125–180.
- Koshy, T. (2001). Fibonacci and Lucas Numbers with Applications, USA: Wiley.
- Luca, F. & Oyono, R. (2011). An exponential Diophantine equation related to powers of two consecutive Fibonacci numbers. Proc Japan Acad., 87 (A), 45–50.
- Shorey, T. N. & Stewart, C. L. (1987). Pure powers in recurrence sequences and some related Diophantine equations. J. Number Theory, 27 (3), 324–352.

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## Cite this paper

APAIrmak, N., & He, B. (2019). *s*-th power of Fibonacci number of the form 2^{a} + 3^{b} + 5^{c}. Notes on Number Theory and Discrete Mathematics, 25(4), 102-109, doi: 10.7546/nntdm.2019.25.4.102-109.

Irmak, Nurettin and Bo He. “*s*-th Power of Fibonacci Number of the Form 2^{a} + 3^{b} + 5^{c}.” Notes on Number Theory and Discrete Mathematics 25, no. 4 (2019): 102-109, doi: 10.7546/nntdm.2019.25.4.102-109.

Irmak, Nurettin and Bo He. “*s*-th Power of Fibonacci Number of the Form 2^{a} + 3^{b} + 5^{c}.” Notes on Number Theory and Discrete Mathematics 25.4 (2019): 102-109. Print, doi: 10.7546/nntdm.2019.25.4.102-109.