MathDB
Problems
Contests
National and Regional Contests
China Contests
China National Olympiad
2021 China National Olympiad
6
China MO 2021 P6
China MO 2021 P6
Source: CMO 2021 P6
November 25, 2020
CMO 2021
number theory
algebra
functional equation
Problem Statement
Find
f
:
Z
+
→
Z
+
f: \mathbb{Z}_+ \rightarrow \mathbb{Z}_+
f
:
Z
+
→
Z
+
, such that for any
x
,
y
∈
Z
+
x,y \in \mathbb{Z}_+
x
,
y
∈
Z
+
,
f
(
f
(
x
)
+
y
)
∣
x
+
f
(
y
)
.
f(f(x)+y)\mid x+f(y).
f
(
f
(
x
)
+
y
)
∣
x
+
f
(
y
)
.
Back to Problems
View on AoPS