Find all sets of positive integers A, B, and C which satisfy

1/A = 1/B + 1/C.

(In reply to

A (partial?) solution by Federico Kereki)

For the general problem 1/A=1/B+1/C+...+1/Z, you can get a solution by picking integer number b, c, ... z, setting A=bc...z, and letting X=A/x.(b+c+...+z).