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2019 APMO
5
Entirely wrapped by f
Entirely wrapped by f
Source: APMO 2019 Problem 05
June 11, 2019
APMO
wrapped
fe
algebra
Problem Statement
Determine all the functions
f
:
R
ā
R
f : \mathbb{R} \to \mathbb{R}
f
:
R
ā
R
such that
f
(
x
2
+
f
(
y
)
)
=
f
(
f
(
x
)
)
+
f
(
y
2
)
+
2
f
(
x
y
)
f(x^2 + f(y)) = f(f(x)) + f(y^2) + 2f(xy)
f
(
x
2
+
f
(
y
))
=
f
(
f
(
x
))
+
f
(
y
2
)
+
2
f
(
x
y
)
for all real numbers
x
x
x
and
y
y
y
.
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