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arXiv · 1811.03015

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

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 $B_{n+1}^x-B_n^x=B_m$ in positive integer variables $(m, n, x)$, where $B_k$ is the $k$-th term of the Balancing sequence.

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Salah E. Rihane, Bernadette Faye, Florian Luca, Alain Togbe. 2018-11-02. An exponential Diophantine equation related to the difference between powers of two consecutive Balancing numbers. https://arxiv.org/abs/1811.03015

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