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arXiv · 2204.08455

On perfect powers that are sum of two balancing numbers

Pritam Kumar Bhoi·Sudhansu Sekhar Rout·Gopal Krishna Panda
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Abstract

Let $B_k$ denote the $k^{th}$ term of balancing sequence. In this paper we find all positive integer solutions of the Diophantine equation $B_n+B_m = x^q$ in variables $(m, n,x,q)$ under the assumption $n\equiv m \pmod 2$. Furthermore, we study the Diophantine equation \[B_n^{3}\pm B_m^{3} = x^q\] with positive integer $q\geq 3$ and $\gcd(B_n, B_m) =1$.

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Pritam Kumar Bhoi, Sudhansu Sekhar Rout, Gopal Krishna Panda. 2022-04-18. On perfect powers that are sum of two balancing numbers. https://doi.org/10.1007/s10998-023-00540-7

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