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1990 Greece National Olympiad
4
f(x+y)=f(x^2)+f(y^2)
f(x+y)=f(x^2)+f(y^2)
Source: 1990 Greece MO Grade XI p4
September 6, 2024
function
algebra
functional
Problem Statement
Find all functions
f
:
R
+
→
R
f: \mathbb{R}^+\to\mathbb{R}
f
:
R
+
→
R
such that
f
(
x
+
y
)
=
f
(
x
2
)
+
f
(
y
2
)
f(x+y)=f(x^2)+f(y^2)
f
(
x
+
y
)
=
f
(
x
2
)
+
f
(
y
2
)
for any
x
,
y
∈
R
+
x,y \in\mathbb{R}^+
x
,
y
∈
R
+
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