Find 4 different positive integers A,B,C,D for which:
A+B = C*D and
A*B = C+D
How many sets of 4 numbers can you find? Prove that only those sets exist.

(A, B, C, D) = (1, 5, 2, 3); (1, 5, 3, 2); (5, 1, 2, 3);(5, 1, 3, 2); (2, 3, 1, 5); (2, 3, 5, 1); (3, 2, 1, 5); (3, 2, 5, 1).

__Note__: When the restriction of all the numbers being distinct is ignored, then we arrive at an additional quadruplet (A ,B, C, , D) = (2,2,2,2) as solution.

*Edited on ***May 19, 2007, 3:58 am**