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2022 Swedish Mathematical Competition
2
f(x + zf(y)) = f(x) + zf(y)
f(x + zf(y)) = f(x) + zf(y)
Source: 2022 Swedish Mathematical Competition p2
March 24, 2024
algebra
functional equation
Problem Statement
Find all functions
f
:
R
→
R
f : R \to R
f
:
R
→
R
such that
f
(
x
+
z
f
(
y
)
)
=
f
(
x
)
+
z
f
(
y
)
,
f(x + zf(y)) = f(x) + zf(y),
f
(
x
+
z
f
(
y
))
=
f
(
x
)
+
z
f
(
y
)
,
for all
x
,
y
,
z
∈
R
x, y, z \in R
x
,
y
,
z
∈
R
.
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