MathDB

2016-2017 Fall OMO Problem 4

Source:

November 16, 2016

Problem Statement

Let

G=10^{10^{100}}

(a.k.a. a googolplex). Then

\log_{\left(\log_{\left(\log_{10} G\right)} G\right)} G

can be expressed in the form

\frac{m}{n}

for relatively prime positive integers

m

and

n

. Determine the sum of the digits of

m+n

.
Proposed by Yannick Yao

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