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4
2016 Japan Mathematical Olympiad Finals, Problem 4
2016 Japan Mathematical Olympiad Finals, Problem 4
Source:
February 14, 2016
Problem Statement
Find all functions
f
:
R
→
R
f: \mathbb{R}\rightarrow \mathbb{R}
f
:
R
→
R
such that
f
(
y
f
(
x
)
−
x
)
=
f
(
x
)
f
(
y
)
+
2
x
f(yf(x)-x)=f(x)f(y)+2x
f
(
y
f
(
x
)
−
x
)
=
f
(
x
)
f
(
y
)
+
2
x
for all
x
,
y
∈
R
x,\ y\in{\mathbb{R}}
x
,
y
∈
R
.
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