Solution of the Diophantine Equation $x_1{x}_2{x}_3\cdots x_{m-1}=z^n$

Abstract

This work determine the entire family of positive integer solutions of the diophantine equation. The solution is described in terms of $\frac{(m-1)(m+n-2)}{2}$ or $\frac{(m-1)(m+n-1)}{2}$ positive parameters depending on $n$ even or odd. We find the solution of a diophantine system of equations by using the solution of the diophantine equation. We generalized all the results of the paper [5].

arXiv commentarXiv admin note: text overlap with arXiv:1307.5328 by other authors