Solution of the Diophantine Equation x1x2x3 · · · xm−1 = z n

Abstract

This work determines the entire family of positive integer solutions of the considered Diophantine equation. The solution is described in terms of (m−1)(m+n−2) 2 or (m−1)(m+n−1) 2 positive parameters depending on the parity of n. The solution of a system of Diophantine equations is also determined with the help of the solution of this Diophantine equation. All the results of the paper [5] are generalized in this paper.