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2010 India IMO Training Camp
11
Indian Team Selection Test 2010 ST4 P2
Indian Team Selection Test 2010 ST4 P2
Source:
May 23, 2010
function
algebra proposed
algebra
Problem Statement
Find all functions
f
:
R
⟶
R
f:\mathbb{R}\longrightarrow\mathbb{R}
f
:
R
⟶
R
such that
f
(
x
+
y
)
+
x
y
=
f
(
x
)
f
(
y
)
f(x+y)+xy=f(x)f(y)
f
(
x
+
y
)
+
x
y
=
f
(
x
)
f
(
y
)
for all reals
x
,
y
x, y
x
,
y
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