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Keywords:
balancing numbers; Pell numbers; Diophantine equation
balancing numbers; Pell numbers; Diophantine equation
Summary:
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 $.
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