There was this dog named Rita
Number Theory
Level
5
Consider the equation
\[\dfrac{1}{a} + \dfrac{1}{b} + \dfrac{1}{c} = \dfrac{1}{d} \]
where \(a, b, c, d\) are distinct positive integers, at least \(3\) of which are prime.
Up to a permutation of the variables, there is a unique solution to this problem. Find \(a + b + c + d\).
by
Brian Charlesworth