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Problems
Contests
National and Regional Contests
Netherlands Contests
Dutch IMO TST
2008 Dutch IMO TST
1
1
Part of
2008 Dutch IMO TST
Problems
(1)
in Z_+ : f(f(f(n))) + f(f(n)) + f(n) = 3n
Source: 2008 Dutch IMO TST P1
1/10/2020
Find all funtions
f
:
Z
>
0
→
Z
>
0
f : Z_{>0} \to Z_{>0}
f
:
Z
>
0
→
Z
>
0
that satisfy
f
(
f
(
f
(
n
)
)
)
+
f
(
f
(
n
)
)
+
f
(
n
)
=
3
n
f(f(f(n))) + f(f(n)) + f(n) = 3n
f
(
f
(
f
(
n
)))
+
f
(
f
(
n
))
+
f
(
n
)
=
3
n
for all
n
∈
Z
>
0
n \in Z_{>0}
n
∈
Z
>
0
.
functional equation
functional equation in N
algebra