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Polish MO Finals
1990 Polish MO Finals
1
functional equation in R
functional equation in R
Source: Problem 1, Polish NO 1990
September 30, 2005
function
algebra
functional equation
algebra unsolved
Problem Statement
Find all functions
f
:
R
⟶
R
f : \mathbb{R} \longrightarrow \mathbb{R}
f
:
R
⟶
R
that satisfy
(
x
−
y
)
f
(
x
+
y
)
−
(
x
+
y
)
f
(
x
−
y
)
=
4
x
y
(
x
2
−
y
2
)
(x - y)f(x + y) - (x + y)f(x - y) = 4xy(x^2 - y^2)
(
x
−
y
)
f
(
x
+
y
)
−
(
x
+
y
)
f
(
x
−
y
)
=
4
x
y
(
x
2
−
y
2
)
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