MathDB
Problems
Contests
International Contests
Balkan MO Shortlist
2021 Balkan MO Shortlist
A6
BMO Shortlist 2021 A6
BMO Shortlist 2021 A6
Source: BMO Shortlist 2021
May 8, 2022
Balkan
shortlist
2021
algebra
functional equation
Problem Statement
Find all functions
f
:
R
→
R
f: \mathbb{R} \rightarrow \mathbb{R}
f
:
R
→
R
such that
f
(
x
y
)
=
f
(
x
)
f
(
y
)
+
f
(
f
(
x
+
y
)
)
f(xy) = f(x)f(y) + f(f(x + y))
f
(
x
y
)
=
f
(
x
)
f
(
y
)
+
f
(
f
(
x
+
y
))
holds for all
x
,
y
∈
R
x, y \in \mathbb{R}
x
,
y
∈
R
.
Back to Problems
View on AoPS