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National and Regional Contests
Netherlands Contests
Dutch IMO TST
2017 Dutch IMO TST
4
functional equation
functional equation
Source: Netherlands TST for IMO 2017 day 2 problem 4
February 1, 2018
functional equation
algebra
Problem Statement
Find all functions
f
:
R
→
R
f : \mathbb{R} \rightarrow \mathbb{R}
f
:
R
→
R
such that
(
y
+
1
)
f
(
x
)
+
f
(
x
f
(
y
)
+
f
(
x
+
y
)
)
=
y
(y + 1)f(x) + f(xf(y) + f(x + y))= y
(
y
+
1
)
f
(
x
)
+
f
(
x
f
(
y
)
+
f
(
x
+
y
))
=
y
for all
x
,
y
∈
R
x, y \in \mathbb{R}
x
,
y
∈
R
.
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