MathDB
Problems
Contests
International Contests
Baltic Way
2020 Baltic Way
4
Good old functional equation on the reals
Good old functional equation on the reals
Source: Baltic Way 2020, Problem 4
November 14, 2020
algebra
Baltic Way
functional equation
Problem Statement
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
.
Back to Problems
View on AoPS