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A Most Unusual Evaluation (Posted on 20060104) 

Let F be an increasing real function defined for all real X, where 0<=X<=1 such that:
(i) F (X/8) = F(X)/7 and
(ii) F(1X) = 1 – F(X)
For all whole numbers M and N greater than zero, determine:
F ( 1/ ((8^M)* ( 8^N + 1)) ) in terms of M and N.
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