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Netherlands Contests
Dutch IMO TST
2011 Dutch IMO TST
2
xf(x + xy) = xf(x) + f(x^2)f(y)
xf(x + xy) = xf(x) + f(x^2)f(y)
Source: Dutch IMO TST2 2011 p2
January 10, 2020
functional equation
algebra
Problem Statement
Find all functions
f
:
R
→
R
f : R\to R
f
:
R
→
R
satisfying
x
f
(
x
+
x
y
)
=
x
f
(
x
)
+
f
(
x
2
)
f
(
y
)
xf(x + xy) = xf(x) + f(x^2)f(y)
x
f
(
x
+
x
y
)
=
x
f
(
x
)
+
f
(
x
2
)
f
(
y
)
for all
x
,
y
∈
R
x, y \in R
x
,
y
∈
R
.
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