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Balkan MO Shortlist
2023 Balkan MO Shortlist
A3
Reals to reals FE
Reals to reals FE
Source: BMO SL 2023 A3
May 3, 2024
algebra
BMO Shortlist
functional equation
Problem Statement
Find all functions
f
:
R
ā
R
f:\mathbb{R} \rightarrow \mathbb{R}
f
:
R
ā
R
, such that
f
(
x
y
+
f
(
x
2
)
)
=
x
f
(
x
+
y
)
f(xy+f(x^2))=xf(x+y)
f
(
x
y
+
f
(
x
2
))
=
x
f
(
x
+
y
)
for all reals
x
,
y
x, y
x
,
y
.
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