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Middle European Mathematical Olympiad
2017 Middle European Mathematical Olympiad
1
Functional equation on the set of reals
Functional equation on the set of reals
Source: MEMO 2017 I1
August 25, 2017
algebra
functional equation
Problem Statement
Determine all functions
f
:
R
ā
R
f : \mathbb{R} \to \mathbb{R}
f
:
R
ā
R
satisfying
f
(
x
2
+
f
(
x
)
f
(
y
)
)
=
x
f
(
x
+
y
)
f(x^2 + f(x)f(y)) = xf(x + y)
f
(
x
2
+
f
(
x
)
f
(
y
))
=
x
f
(
x
+
y
)
for all real numbers
x
x
x
and
y
y
y
.
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