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On solutions of the diophantine equation \(\varvec{F_{n}-F_{m}=3^{a}}\)

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Abstract

In this paper, we find non-negative (n, m, a) integer solutions of the diophantine equation \(F_{n}-F_{m}=3^{a}\), where \(F_{n}\) and \(F_{m}\) are Fibonacci numbers. For proving our theorem, we use lower bounds in linear forms.

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Authors and Affiliations

  1. Department of Fundamental Sciences, Izmir Bakırçay University, Izmir, Turkey

    Bahar Demirtürk Bitim

  2. Department of Mathematics, Sakarya University, Adapazarı, Turkey

    Refik Keskin

Authors
  1. Bahar Demirtürk Bitim
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  2. Refik Keskin
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Correspondence to Bahar Demirtürk Bitim.

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Communicating Editor: Sanoli Gun

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Bitim, B.D., Keskin, R. On solutions of the diophantine equation \(\varvec{F_{n}-F_{m}=3^{a}}\). Proc Math Sci 129, 81 (2019). https://doi.org/10.1007/s12044-019-0524-6

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  • DOI: https://doi.org/10.1007/s12044-019-0524-6

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