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Pan African
2002 Pan African
1
f(f(n))=f(n)+1 with minimum 1
f(f(n))=f(n)+1 with minimum 1
Source: Pan African 2002
August 20, 2005
function
Problem Statement
Find all functions
f
:
N
0
→
N
0
f: N_0 \to N_0
f
:
N
0
→
N
0
, (where
N
0
N_0
N
0
is the set of all non-negative integers) such that
f
(
f
(
n
)
)
=
f
(
n
)
+
1
f(f(n))=f(n)+1
f
(
f
(
n
))
=
f
(
n
)
+
1
for all
n
∈
N
0
n \in N_0
n
∈
N
0
and the minimum of the set
{
f
(
0
)
,
f
(
1
)
,
f
(
2
)
⋯
}
\{ f(0), f(1), f(2) \cdots \}
{
f
(
0
)
,
f
(
1
)
,
f
(
2
)
⋯
}
is
1
1
1
.
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