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Balkan MO
2021 Balkan MO
2
2
Part of
2021 Balkan MO
Problems
(1)
BMO 2021 problem 2
Source: Balkan MO 2021 P2
9/8/2021
Find all functions
f
:
R
+
ā
R
+
f: \mathbb{R}^{+} \rightarrow \mathbb{R}^{+}
f
:
R
+
ā
R
+
, such that
f
(
x
+
f
(
x
)
+
f
(
y
)
)
=
2
f
(
x
)
+
y
f(x+f(x)+f(y))=2f(x)+y
f
(
x
+
f
(
x
)
+
f
(
y
))
=
2
f
(
x
)
+
y
for all positive reals
x
,
y
x,y
x
,
y
.Proposed by Athanasios Kontogeorgis, Greece
functional equation
algebra
Balkan Mathematics Olympiad