Determine all possible nonzero integers A and B, with A ≠ B, that satisfy this equation.

                                         A^B = B^A-B

There are at least six pairs of integers (A,B) that satisfy the equation A^B = B^A-B:
(-8,-2), (1,-1), (0,0), (1,1), (8,2), and (9,3).

(0,0) and (1,1) satisfy the equation, yet the set (0,0) is not a set of non-zero integers, and both (0,0) and (1,1) are cases where A = B, thus neither are one of set of values that is part of the final solution. 

Edited on July 20, 2008, 7:40 pm

Posted by Dej Mar on 2008-07-19 22:32:45