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3
Polish MO Finals 2018, Problem 3
Polish MO Finals 2018, Problem 3
Source:
April 18, 2018
functional equation
algebra
Poland
TST
Problem Statement
Find all real numbers
c
c
c
for which there exists a function
f
:
R
→
R
f\colon\mathbb R\rightarrow \mathbb R
f
:
R
→
R
such that for each
x
,
y
∈
R
x, y\in\mathbb R
x
,
y
∈
R
it's true that
f
(
f
(
x
)
+
f
(
y
)
)
+
c
x
y
=
f
(
x
+
y
)
.
f(f(x)+f(y))+cxy=f(x+y).
f
(
f
(
x
)
+
f
(
y
))
+
c
x
y
=
f
(
x
+
y
)
.
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