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Baltic Way
2010 Baltic Way
5
Find all functions
Find all functions
Source: Baltic Way 2010
November 19, 2010
function
algebra proposed
algebra
Problem Statement
Let
R
\mathbb{R}
R
denote the set of real numbers. Find all functions
f
:
R
→
R
f:\mathbb{R}\rightarrow\mathbb{R}
f
:
R
→
R
such that
f
(
x
2
)
+
f
(
x
y
)
=
f
(
x
)
f
(
y
)
+
y
f
(
x
)
+
x
f
(
x
+
y
)
f(x^2)+f(xy)=f(x)f(y)+yf(x)+xf(x+y)
f
(
x
2
)
+
f
(
x
y
)
=
f
(
x
)
f
(
y
)
+
y
f
(
x
)
+
x
f
(
x
+
y
)
for all
x
,
y
∈
R
x,y\in\mathbb{R}
x
,
y
∈
R
.
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