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Balkan MO
2000 Balkan MO
1
1
Part of
2000 Balkan MO
Problems
(1)
Find all functions
Source: Balkan MO 2000, problem 1 and 1997, problem 4 (!!)
10/16/2005
Find all functions
f
:
R
→
R
f: \mathbb R \to \mathbb R
f
:
R
→
R
such that
f
(
x
f
(
x
)
+
f
(
y
)
)
=
f
2
(
x
)
+
y
f( xf(x) + f(y) ) = f^2(x) + y
f
(
x
f
(
x
)
+
f
(
y
))
=
f
2
(
x
)
+
y
for all
x
,
y
∈
R
x,y\in \mathbb R
x
,
y
∈
R
.
algebra
functional equation
Balkan Mathematics Olympiad