Pritam Kumar Bhoi, Sudhansu Sekhar Rout, Gopal Krishna Panda
Published 2022-04-18Version 1
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 $(m, n,x,q)$ under the assumption $n\equiv m \pmod 2$. Furthermore, we study the Diophantine equation \[B_n^{3}\pm B_m^{3} = x^q\] with positive integer $q\geq 3$ and $\gcd(B_n, B_m) =1$.
General Terms of All Almost Balancing Numbers of First and Second Type
Solution of the Diophantine Equation $ x_{1}x_{2}x_{3}\cdots x_{m-1}=z^n $
The Diophantine Equation x^n+y^m=c(x^k)(y^l), n,m,k,l,c natural numbers
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