ON THE DIOPHANTINE EQUATION $\frac{1}{x}+\frac{3}{y}+\frac{5}{z}=\frac{3}{4}}$

Abstract

In this paper, we show that the Diophantine equation $\frac{1}{x}+\frac{3}{y}+\frac{5}{z}=\frac{3}{4}$ has finitely many integral solutions in the positive integers $x,y$ and $z$.