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2022-IMOC
A3
xy(f(x+y)-f(x)-f(y))=2f(xy)
xy(f(x+y)-f(x)-f(y))=2f(xy)
Source: 2022 IMOC A3
September 5, 2022
algebra
function
functional equation
Problem Statement
Find all functions
f
:
R
→
R
f:\mathbb R\to \mathbb R
f
:
R
→
R
such that
x
y
(
f
(
x
+
y
)
−
f
(
x
)
−
f
(
y
)
)
=
2
f
(
x
y
)
xy(f(x+y)-f(x)-f(y))=2f(xy)
x
y
(
f
(
x
+
y
)
−
f
(
x
)
−
f
(
y
))
=
2
f
(
x
y
)
for all
x
,
y
∈
R
.
x,y\in \mathbb R.
x
,
y
∈
R
.
Proposed by USJL
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