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China Team Selection Test
2024 China Team Selection Test
5
FE in TST
FE in TST
Source: 2024 CTST P5
March 7, 2024
algebra
functional equation
2024 CTST
Problem Statement
Find all functions
f
:
N
+
→
N
+
,
f:\mathbb N_+\to \mathbb N_+,
f
:
N
+
→
N
+
,
such that for all positive integer
a
,
b
,
a,b,
a
,
b
,
∑
k
=
0
2
b
f
(
a
+
k
)
=
(
2
b
+
1
)
f
(
f
(
a
)
+
b
)
.
\sum_{k=0}^{2b}f(a+k)=(2b+1)f(f(a)+b).
k
=
0
∑
2
b
f
(
a
+
k
)
=
(
2
b
+
1
)
f
(
f
(
a
)
+
b
)
.
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