On the Diophantine Equation 1/w+1/x+1/y+1/z=u/u+1

In 2023, Wongsanurak and Duangdai found all positive integer solutions of the Diophantine equation , when and are positive integers with and . In this work, by using an elementary approach, we solved the Diophantine equation for any positive integer and . The results of the research found that the Diophantine equation under the above conditions has twenty-seven positive integer solutions.