Geodesic
On some Diophantine equations involving balancing numbers
Archivum mathematicum, Tome 57 (2021) no. 2, pp. 113-130 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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In this paper, we find all the solutions of the Diophantine equation $B_1^p+2B_2^p+\cdots +kB_k^p=B_n^q$ in positive integer variables $(k, n)$, where $B_i$ is the $i^{th}$ balancing number if the exponents $p$, $ q$ are included in the set $\lbrace 1,2\rbrace $.
In this paper, we find all the solutions of the Diophantine equation $B_1^p+2B_2^p+\cdots +kB_k^p=B_n^q$ in positive integer variables $(k, n)$, where $B_i$ is the $i^{th}$ balancing number if the exponents $p$, $ q$ are included in the set $\lbrace 1,2\rbrace $.
DOI : 10.5817/AM2021-2-113
Classification : 11B39
Keywords: balancing numbers; Pell numbers; Diophantine equation 
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Tchammou, Euloge; Togbé, Alain. On some Diophantine equations involving balancing numbers. Archivum mathematicum, Tome 57 (2021) no. 2, pp. 113-130. doi: 10.5817/AM2021-2-113

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