Each of F, G and H are positive integers such that:

F^GH* G^HF* H^FG = 5*F*G*H

Determine the possible value(s) that F+G+H can assume.

Note: For a precise interpretation of the value of A^BC, refer to the wikipedia article on exponentiation in this location.

F^(G^H-1)*G^(H^F-1)*H^(F^G-1) = 5
It is cyclic so assume F>G>H
So F^(G^H-1)=5 and G^(H^F-1)=1 and H^(F^G-1)=1
F=5 and G^H-1 = 1,So, G^H=2 => G=2 and H=1
This satisfies the other 2 equations.
So, F+G+H can take only 8 its value

 

Posted by Praneeth on 2008-02-14 03:18:30