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Italy TST
2007 Italy TST
3
Nice functional equation
Nice functional equation
Source: Italian TST , day 1, n°3
June 1, 2007
function
algebra
polynomial
algebra proposed
functional equation
Problem Statement
Find all
f
:
R
⟶
R
f: R \longrightarrow R
f
:
R
⟶
R
such that
f
(
x
y
+
f
(
x
)
)
=
x
f
(
y
)
+
f
(
x
)
f(xy+f(x))=xf(y)+f(x)
f
(
x
y
+
f
(
x
))
=
x
f
(
y
)
+
f
(
x
)
for every pair of real numbers
x
,
y
x,y
x
,
y
.
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