Abstract
In this paper, we find all the balancing numbers which are sum of same power of consecutive balancing numbers. For this, we find all the solutions of the Diophantine equation \({B_{n}^{x}}+B_{n+1}^{x}+{\cdots } +B_{n+k-1}^{x}=B_{m}\) in positive integers (m,n,k,x), where Bi is the i th term of the balancing sequence.
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Acknowledgements
The first two authors are supported by IMSP, Institut de Mathématiques et de Sciences Physiques de l’Université d’Abomey-Calavi. This paper is completed when the third author visited the University of Ghana. He thanks the authorities for the warm hospitality and the working environment.
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Nansoko, S., Tchammou, E. & Togbé, A. Balancing Numbers as Sum of Same Power of Consecutive Balancing Numbers. Vietnam J. Math. 52, 75–88 (2024). https://doi.org/10.1007/s10013-022-00573-4
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DOI: https://doi.org/10.1007/s10013-022-00573-4