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Switzerland - Final Round
2006 Switzerland - Final Round
1
1
Part of
2006 Switzerland - Final Round
Problems
(1)
yf(2x) - xf(2y) = 8xy(x^2 - y^2)
Source: Switzerland - 2006 Swiss MO Final Round p1
12/26/2022
Find all functions
f
:
R
→
R
f : R \to R
f
:
R
→
R
such that for all
x
,
y
∈
R
x, y \in R
x
,
y
∈
R
holds
y
f
(
2
x
)
−
x
f
(
2
y
)
=
8
x
y
(
x
2
−
y
2
)
.
yf(2x) - xf(2y) = 8xy(x^2 - y^2).
y
f
(
2
x
)
−
x
f
(
2
y
)
=
8
x
y
(
x
2
−
y
2
)
.
functional
functional equation
algebra