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Mathematics
Mathematics
Problem
Let
f
(
n
)
f(n)
f
(
n
)
denotes the square of the sum of the digits of natural number
n
n
n
, where
f
2
(
n
)
f^2(n)
f
2
(
n
)
denotes
f
(
f
(
n
)
)
f(f(n))
f
(
f
(
n
))
,
f
3
(
n
)
f^3(n)
f
3
(
n
)
denotes
f
(
f
(
f
(
n
)
)
)
f(f(f(n)))
f
(
f
(
f
(
n
)))
and so on. The value of
f
2011
(
2011
)
−
f
2010
(
2011
)
f
2013
(
2011
)
−
f
2012
(
2011
)
is .....
\frac{f^{2011}(2011) - f^{2010}(2011)}{f^{2013}(2011) - f^{2012}(2011)} \text{ is .....}
f
2013
(
2011
)
−
f
2012
(
2011
)
f
2011
(
2011
)
−
f
2010
(
2011
)
is .....
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