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Baltic Way
2023 Baltic Way
4
R to R FE
R to R FE
Source: Baltic Way 2023/4
November 11, 2023
algebra
Problem Statement
Find all functions
f
:
R
ā
R
f: \mathbb{R} \rightarrow \mathbb{R}
f
:
R
ā
R
such that
f
(
f
(
x
)
+
y
)
+
x
f
(
y
)
=
f
(
x
y
+
y
)
+
f
(
x
)
f(f(x)+y)+xf(y)=f(xy+y)+f(x)
f
(
f
(
x
)
+
y
)
+
x
f
(
y
)
=
f
(
x
y
+
y
)
+
f
(
x
)
for reals
x
,
y
x, y
x
,
y
.
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