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Balkan MO Shortlist
2022 Balkan MO Shortlist
A1
A1
Part of
2022 Balkan MO Shortlist
Problems
(1)
Simple FE
Source: BMO Shortlist 2022, A1
5/13/2023
Find all functions
f
:
R
→
R
f : \mathbb{R} \to \mathbb{R}
f
:
R
→
R
such that
f
(
x
(
x
+
f
(
y
)
)
)
=
(
x
+
y
)
f
(
x
)
,
f(x(x + f(y))) = (x + y)f(x),
f
(
x
(
x
+
f
(
y
)))
=
(
x
+
y
)
f
(
x
)
,
for all
x
,
y
∈
R
x, y \in\mathbb{R}
x
,
y
∈
R
.
algebra
functional equation
BMO Shortlist