Each of P, Q, R, and S is a positive integer with P<Q<R<S.

Find the quadruplets (P, Q, R, S) that satisfy this equation:

         1/P + 1/Q + 1/R + 1/S = 1

Prove that these are the only possible quadruplets that satisfy the given conditions.

Note: Computer program solutions are welcome, but a semi-analytical solution is preferred.