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2011 International Zhautykov Olympiad
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International Zhautykov Olympiad 2011 - Problem 2
International Zhautykov Olympiad 2011 - Problem 2
Source:
January 16, 2011
function
algebra
functional equation
algebra unsolved
Problem Statement
Find all functions
f
:
R
→
R
f:\mathbb{R}\rightarrow\mathbb{R}
f
:
R
→
R
which satisfy the equality,
f
(
x
+
f
(
y
)
)
=
f
(
x
−
f
(
y
)
)
+
4
x
f
(
y
)
f(x+f(y))=f(x-f(y))+4xf(y)
f
(
x
+
f
(
y
))
=
f
(
x
−
f
(
y
))
+
4
x
f
(
y
)
for any
x
,
y
∈
R
x,y\in\mathbb{R}
x
,
y
∈
R
.
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