MathDB
Problems
Contests
International Contests
Balkan MO Shortlist
2021 Balkan MO Shortlist
A5
BMO Shortlist 2021 A5
BMO Shortlist 2021 A5
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
f
(
x
+
y
)
)
=
y
f
(
x
)
+
1
f(xf(x + y)) = yf(x) + 1
f
(
x
f
(
x
+
y
))
=
y
f
(
x
)
+
1
holds for all
x
,
y
∈
R
+
x, y \in \mathbb{R}^{+}
x
,
y
∈
R
+
.Proposed by Nikola Velov, North Macedonia
Back to Problems
View on AoPS