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2024-IMOC
A4
Third degree FE
Third degree FE
Source: 2024 IMOC A4 (Boring Competition P2)
August 8, 2024
algebra
functional equation
Problem Statement
find all function
f
:
R
→
R
f:\mathbb{R} \to \mathbb{R}
f
:
R
→
R
such that
f
(
x
3
−
x
f
(
y
)
2
)
=
x
f
(
x
+
y
)
f
(
x
−
y
)
f(x^3-xf(y)^2)=xf(x+y)f(x-y)
f
(
x
3
−
x
f
(
y
)
2
)
=
x
f
(
x
+
y
)
f
(
x
−
y
)
holds for all real number
x
x
x
,
y
y
y
.Proposed by chengbilly
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