Determine all possible quadruplet(s) (A,B,C,D) of positive integers, with A ≤ C, that satisfy this system of equations:

A*(B-1)= C+D, and:

C*(D-1) = A+B

Prove that these are the only quadruplet(s) that exist.

The following satisfy the equations:

A  B  C  D

1  9  2  6

1  8  3  4

1  9  5  3

2  4  2  4

2  4  3  3

2  6  8  2

3  3  3  3

3  4  7  2

5  3  8  2

(A <= C the only restriction)

 

Posted by ed bottemiller on 2010-06-09 15:04:50