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Balkan MO Shortlist
2023 Balkan MO Shortlist
A6
Positive reals FE with x^2023
Positive reals FE with x^2023
Source: BMO SL 2023 A6
May 3, 2024
algebra
Problem Statement
Find all functions
f
:
R
+
ā
R
+
f:\mathbb{R}^+ \rightarrow \mathbb{R}^+
f
:
R
+
ā
R
+
, such that
f
(
x
2023
+
f
(
x
)
f
(
y
)
)
=
x
2023
+
y
f
(
x
)
f(x^{2023}+f(x)f(y))=x^{2023}+yf(x)
f
(
x
2023
+
f
(
x
)
f
(
y
))
=
x
2023
+
y
f
(
x
)
for all
x
,
y
>
0
x, y>0
x
,
y
>
0
.
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