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Balkan MO
2022 Balkan MO
3
3
Part of
2022 Balkan MO
Problems
(1)
Cubed FE
Source: Balkan MO 2022 P3
5/6/2022
Find all functions
f
:
(
0
,
∞
)
→
(
0
,
∞
)
f: (0, \infty) \to (0, \infty)
f
:
(
0
,
∞
)
→
(
0
,
∞
)
such that \begin{align*} f(y(f(x))^3 + x) = x^3f(y) + f(x) \end{align*} for all
x
,
y
>
0
x, y>0
x
,
y
>
0
. Proposed by Jason Prodromidis, Greece
Balkan Mathematics Olympiad
functional equation
algebra