On perfect powers that are sum of two balancing numbers

Pritam Kumar Bhoi, Sudhansu Sekhar Rout, Gopal Krishna Panda

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 $(m,n,x,q)$…