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National and Regional Contests
Vietnam Contests
Vietnam National Olympiad
2021 Vietnam National Olympiad
2
VMO 2021, P2
VMO 2021, P2
Source:
December 25, 2020
function
algebra
functional equation
VMO 2020-2021
National Olympiads
Problem Statement
Find all function
f
:
R
→
R
f:\mathbb{R}\to \mathbb{R}
f
:
R
→
R
such that
f
(
x
)
f
(
y
)
=
f
(
x
y
−
1
)
+
y
f
(
x
)
+
x
f
(
y
)
f(x)f(y)=f(xy-1)+yf(x)+xf(y)
f
(
x
)
f
(
y
)
=
f
(
x
y
−
1
)
+
y
f
(
x
)
+
x
f
(
y
)
for all
x
,
y
∈
R
x,y \in \mathbb{R}
x
,
y
∈
R
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