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2022 Azerbaijan BMO TST
A2
f (x + yf(x + y))= y^2 + f(x)f(y)
f (x + yf(x + y))= y^2 + f(x)f(y)
Source: 2021 Dutch IMO TST 3.3
December 28, 2021
functional
functional equation
algebra
Problem Statement
Find all functions
f
:
R
→
R
f : R \to R
f
:
R
→
R
with
f
(
x
+
y
f
(
x
+
y
)
)
=
y
2
+
f
(
x
)
f
(
y
)
f (x + yf(x + y))= y^2 + f(x)f(y)
f
(
x
+
y
f
(
x
+
y
))
=
y
2
+
f
(
x
)
f
(
y
)
for all
x
,
y
∈
R
x, y \in R
x
,
y
∈
R
.
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