Integer Solutions of the Diophantine Equation \(\left (1-\frac{1}{\mathit{x}}\right)\) \(\left (1-\frac{1}{\mathit{y}}\right)\) \(\left (1-\frac{1}{\mathit{z}}\right)\) = \(\frac{1}{\mathit{l}}\)

Abstract

In this paper, we mainly find all solutions of the diophantine equation \(\left (1-\frac{1}{\mathit{x}}\right)\) \(\left (1-\frac{1}{\mathit{y}}\right)\) \(\left (1-\frac{1}{\mathit{z}}\right)\) = \(\frac{1}{\mathit{l}}\) in integer variables (\(\mathit{x}\), \(\mathit{y}\), \(\mathit{z}\), \(\mathit{l}\) ).