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2003 India IMO Training Camp
3
Find f if f(x+y)+f(x)f(y)=f(xy)+f(x)+f(y)
Find f if f(x+y)+f(x)f(y)=f(xy)+f(x)+f(y)
Source:
January 9, 2011
function
algebra proposed
algebra
Problem Statement
Find all functions
f
:
R
ā
R
f: \mathbb R \to \mathbb R
f
:
R
ā
R
such that for all reals
x
x
x
and
y
y
y
,
f
(
x
+
y
)
+
f
(
x
)
f
(
y
)
=
f
(
x
y
)
+
f
(
x
)
+
f
(
y
)
.
f(x+y)+f(x)f(y)=f(xy)+f(x)+f(y).
f
(
x
+
y
)
+
f
(
x
)
f
(
y
)
=
f
(
x
y
)
+
f
(
x
)
+
f
(
y
)
.
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