Quadruple Reciprocal Sum

Algebra Level 5

How many ordered quadruples of distinct positive integers (a,b,c,d) (a, b, c, d) are there such that 1a+1b+1c+1d=1 \frac {1}{a} + \frac {1}{b} + \frac {1}{c} + \frac {1}{d} = 1?

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