s-th power of Fibonacci number of the form 2a + 3b + 5c

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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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


In this paper, we solve the Diophantine equation F_{n}^{s}=2^{a}+3^{b}+5^{c}, where a,b,c and s are positive integers with 1\le \max \left\{a,b\right\} \leq c.


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

2010 Mathematics Subject Classification

  • 11B39
  • 11J86


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Cite this paper

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

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