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.
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Submitted by K Sengupta
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Rating: 3.5000 (2 votes)
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Solution:
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(Hide)
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I reproduce herewith the solution furnished by Praneeth, albeit with minor corrections.
Solution:
From the given relationship, we obtain:
F(G^H-1)*G(H^F-1)*H(F^G-1) = 5
The given relationship is cyclic, and accordingly without loss of generality one can assume that F>=G>=H
So F(G^H-1) =5 and G(H^F-1)=1 and H(F^G-1)=1
This gives, F=5 and G^H -1 = 1, and so, G^H=2 => G=2 and H=1
Accordingly, in terms of (*), the other possible values of (F, G, H) without the restriction in terms of the assumption are: (2, 1, 5), (1, 5, 2)
F+G+H = 8 is all the above three cases, and consequently, the only possible value that F+G+H can assume is 8.
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