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Japan MO Finals
2004 Japan MO Finals
2
F(xf(x)+f(y))=(f(x))^2+y
F(xf(x)+f(y))=(f(x))^2+y
Source: Japan Mathematical Olympiad Finals 2004, Problem 2
November 7, 2005
function
algebra proposed
algebra
Problem Statement
Find all functions
f
:
R
↦
R
f : \mathbb{R} \mapsto \mathbb{R}
f
:
R
↦
R
such that
f
(
x
f
(
x
)
+
f
(
y
)
)
=
(
f
(
x
)
)
2
+
y
f(xf(x)+f(y)) =(f(x))^2+y
f
(
x
f
(
x
)
+
f
(
y
))
=
(
f
(
x
)
)
2
+
y
for all
x
,
y
∈
R
.
\ x,y \in \mathbb{R}.
x
,
y
∈
R
.
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