Address:
Institut de Mathématiques et de Sciences Physiques, Dangbo, Bénin
Department of Mathematics and Statistics, Purdue University Northwest, 1401 S, U.S. 421, Westville IN 46391 USA
E-mail:
euloge.tchammou@imsp-uac.org
atogbe@pnw.edu
Abstract: 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 $.
AMSclassification: primary 11B39.
Keywords: balancing numbers, Pell numbers, Diophantine equation.
DOI: 10.5817/AM2021-2-113