Reciprocal sum is exactly 1 now

Number Theory Level 4

Find the number of solutions to the equation \[\frac{1}{a}+ \frac{1}{b}+ \frac{1}{c} +\frac{1}{d}=1\] where \(a,\ b,\ c,\ d\) are positive integers and \(a\leq b \leq c \leq d.\)