The Natural Number Solution of Diophantine Equation 1/w + 1/x + 1/y + 1/z = u/(u+1)

Abstract

In this research, the solutions of the Diophantine equation in the form 1/w + 1/x + 1/y + 1/z = u/(u+1) were studied, where w<=x<=y<=z and u.=> 1 . Considering only the values of w, x, y, and z as non-negative integers, the study found that there are a total of 18 solutions where the results are single-digit numbers. From all the solutions, it was concluded that the value of u = 6 cannot be obtained, and it is not possible to find values for w, x, y, and z that are non-negative integers and single-digit numbers.