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Korea National Olympiad
2020 Korea National Olympiad
1
Another FE
Another FE
Source: 2020 Korea National Olympiad P1
November 21, 2020
function
algebra
functional equation
Problem Statement
Determine all functions
f
:
R
→
R
f:\mathbb{R}\rightarrow\mathbb{R}
f
:
R
→
R
such that
x
2
f
(
x
)
+
y
f
(
y
2
)
=
f
(
x
+
y
)
f
(
x
2
−
x
y
+
y
2
)
x^2f(x)+yf(y^2)=f(x+y)f(x^2-xy+y^2)
x
2
f
(
x
)
+
y
f
(
y
2
)
=
f
(
x
+
y
)
f
(
x
2
−
x
y
+
y
2
)
for all
x
,
y
∈
R
x,y\in\mathbb{R}
x
,
y
∈
R
.
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