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National and Regional Contests
PEN Problems
PEN K Problems
7
K 7
K 7
Source:
May 25, 2007
function
Functional Equations
Problem Statement
Find all functions
f
:
N
→
N
f: \mathbb{N}\to \mathbb{N}
f
:
N
→
N
such that for all
n
∈
N
n\in \mathbb{N}
n
∈
N
:
f
(
f
(
n
)
)
+
f
(
n
)
=
2
n
+
2001
or
2
n
+
2002.
f(f(n))+f(n)=2n+2001 \text{ or }2n+2002.
f
(
f
(
n
))
+
f
(
n
)
=
2
n
+
2001
or
2
n
+
2002.
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