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An exponential Diophantine equation related to the difference between powers of two consecutive Balancing numbers

Number Theory 2018-11-08 v1
Authors: Salah E. Rihane , Bernadette Faye , Florian Luca , Alain Togbe
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Abstract

In this paper, we find all solutions of the exponential Diophantine equation Bn+1x−Bnx=BmB_{n+1}^x-B_n^x=B_m in positive integer variables (m,n,x)(m, n, x), where BkB_k is the kk-th term of the Balancing sequence.

Keywords

exponential diophantine equation balancing numbers integer solutions balancing sequence

Cite

@article{arxiv.1811.03015,
  title  = {An exponential Diophantine equation related to the difference between powers of two consecutive Balancing numbers},
  author = {Salah E. Rihane and Bernadette Faye and Florian Luca and Alain Togbe},
  journal= {arXiv preprint arXiv:1811.03015},
  year   = {2018}
}

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