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Baltic Way
2020 Baltic Way
4
4
Part of
2020 Baltic Way
Problems
(1)
Good old functional equation on the reals
Source: Baltic Way 2020, Problem 4
11/14/2020
Find all functions
f
:
R
ā
R
f:\mathbb{R} \to \mathbb{R}
f
:
R
ā
R
so that
f
(
f
(
x
)
+
x
+
y
)
=
f
(
x
+
y
)
+
y
f
(
y
)
f(f(x)+x+y) = f(x+y) + y f(y)
f
(
f
(
x
)
+
x
+
y
)
=
f
(
x
+
y
)
+
y
f
(
y
)
for all real numbers
x
,
y
x, y
x
,
y
.
algebra
Baltic Way
functional equation