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, 5, 2), (2, 1, 5), (5, 2, 1)}

1⁵²*2¹⁵*5²¹ = 1²⁵*2¹*5² = 1*2*25 = 50

(5)*1*5*2 = 50

[F + G + H] = 8

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Note, though only 1, 2, and 5 are the integers that are the solutions for (F, G, H), not all arrangements of 1, 2, and 5 are, e.g., for (1, 2, 5)...
1²⁵*2⁵¹*5¹² = 1³²*2⁵*5¹ = 1*32*5 = 160

Edited on February 12, 2008, 1:38 pm

Posted by Dej Mar on 2008-02-12 13:38:02