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In this paper, we find all solutions of the exponential Diophantine equation $B_{n+1}^x-B_n^x=B_m$ in positive integer variables $(m, n, x)$, where $B_k$ is the $k$-th term of the Balancing sequence.

az eszterházy károly tanárképző főiskola tudományos közleményei. tanulmányok a matematikai tudományok köréből/az eszterházy károly főiskola tudományos közleményei. tanulmányok a matematikai tudományok köréből/annales mathematicae et informaticae

An exponential Diophantine equation related to the difference between powers of two consecutive Balancing numbers