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2013 Math Prize For Girls Problems
19
19
Part of
2013 Math Prize For Girls Problems
Problems
(1)
Math Prize 2013 Problem 19
Source:
9/10/2013
If
n
n
n
is a positive integer, let
ϕ
(
n
)
\phi(n)
ϕ
(
n
)
be the number of positive integers less than or equal to
n
n
n
that are relatively prime to
n
n
n
. Compute the value of the infinite sum
∑
n
=
1
∞
ϕ
(
n
)
2
n
9
n
−
2
n
.
\sum_{n=1}^\infty \frac{\phi(n) 2^n}{9^n - 2^n} \, .
n
=
1
∑
∞
9
n
−
2
n
ϕ
(
n
)
2
n
.
number theory
relatively prime