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National and Regional Contests
Korea Contests
Korea Winter Program Practice Test
2020 Korean MO winter camp
#7
Another FE
Another FE
Source: 2020 Korean MO winter camp Test 1 P7
September 7, 2020
algebra
Problem Statement
Find all functions
f
:
R
→
R
f:\mathbb{R}\rightarrow\mathbb{R}
f
:
R
→
R
such that
2
f
(
x
2
+
y
2
)
=
(
x
+
f
(
y
)
)
2
+
f
(
x
−
f
(
y
)
)
2
2f(x^2+y^2)=(x+f(y))^2+f(x-f(y))^2
2
f
(
x
2
+
y
2
)
=
(
x
+
f
(
y
)
)
2
+
f
(
x
−
f
(
y
)
)
2
for all
x
,
y
∈
R
x,y\in\mathbb{R}
x
,
y
∈
R
.
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