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National and Regional Contests
Korea Contests
Korea Junior Mathematics Olympiad
2013 Korea Junior Math Olympiad
7
7
Part of
2013 Korea Junior Math Olympiad
Problems
(1)
Function with asymptotic irrational slope
Source: kjmo 2013 pr 7
9/21/2017
Let
f
:
N
⟶
N
f:\mathbb{N} \longrightarrow \mathbb{N}
f
:
N
⟶
N
be such that for every positive integer
n
n
n
, followings are satisfied. i.
f
(
n
+
1
)
>
f
(
n
)
f(n+1) > f(n)
f
(
n
+
1
)
>
f
(
n
)
ii.
f
(
f
(
n
)
)
=
2
n
+
2
f(f(n)) = 2n+2
f
(
f
(
n
))
=
2
n
+
2
Find the value of
f
(
2013
)
f(2013)
f
(
2013
)
. (Here,
N
\mathbb{N}
N
is the set of all positive integers.)
Functional Equations