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Balkan MO
2007 Balkan MO
2
Find function f
Find function f
Source: Balkan olympiad 2007, problem 2.
April 28, 2007
algebra
functional equation
BMO Shortlist
Problem Statement
Find all real functions
f
f
f
defined on
R
\mathbb R
R
, such that
f
(
f
(
x
)
+
y
)
=
f
(
f
(
x
)
ā
y
)
+
4
f
(
x
)
y
,
f(f(x)+y) = f(f(x)-y)+4f(x)y ,
f
(
f
(
x
)
+
y
)
=
f
(
f
(
x
)
ā
y
)
+
4
f
(
x
)
y
,
for all real numbers
x
,
y
x,y
x
,
y
.
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