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Problems
Contests
International Contests
Pan African
2003 Pan African
1
functional equation
functional equation
Source: Pan African 2003
October 4, 2005
function
functional equation
Problem Statement
Let
N
0
=
{
0
,
1
,
2
⋯
}
\mathbb{N}_0=\{0,1,2 \cdots \}
N
0
=
{
0
,
1
,
2
⋯
}
. Does there exist a function f: \mathbb{N}__0 \to \mathbb{N}_0 such that:
f
2003
(
n
)
=
5
n
,
∀
n
∈
N
0
f^{2003}(n)=5n, \forall n \in \mathbb{N}_0
f
2003
(
n
)
=
5
n
,
∀
n
∈
N
0
where we define:
f
1
(
n
)
=
f
(
n
)
f^1(n)=f(n)
f
1
(
n
)
=
f
(
n
)
and
f
k
+
1
(
n
)
=
f
(
f
k
(
n
)
)
f^{k+1}(n)=f(f^k(n))
f
k
+
1
(
n
)
=
f
(
f
k
(
n
))
,
∀
k
∈
N
0
\forall k \in \mathbb{N}_0
∀
k
∈
N
0
?
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