Determine all possible positive real triplets (a, b, c) satisfying a^b =c; b^c = a and c^a = b

Using OOO's explanation abc=1:

The problem states all are positive. Then, if a>1, then b<1 or c<1 (or both). Since c^a=b, and a>1 then c<b. So c<1, and thus so must b<1. However, since b^c=a, this implies a<1

Posted by Gamer on 2007-06-08 23:53:55