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European Mathematical Cup 2016 problem 3 senior division
European Mathematical Cup 2016 problem 3 senior division
Source:
December 31, 2016
algebra
Problem Statement
Determine all functions
f
:
R
ā
R
f:\mathbb R\to\mathbb R
f
:
R
ā
R
such that equality
f
(
x
+
y
+
y
f
(
x
)
)
=
f
(
x
)
+
f
(
y
)
+
x
f
(
y
)
f(x + y + yf(x)) = f(x) + f(y) + xf(y)
f
(
x
+
y
+
y
f
(
x
))
=
f
(
x
)
+
f
(
y
)
+
x
f
(
y
)
holds for all real numbers
x
x
x
,
y
y
y
.Proposed by Athanasios Kontogeorgis
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