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Albanian IMO TST 2010 Question 2
Albanian IMO TST 2010 Question 2
Source:
May 22, 2010
function
induction
algebra
domain
functional equation
algebra unsolved
Problem Statement
Find all the continuous functions
f
:
R
↦
R
f : \mathbb{R} \mapsto\mathbb{R}
f
:
R
↦
R
such that
∀
x
,
y
∈
R
\forall x,y \in \mathbb{R}
∀
x
,
y
∈
R
,
(
1
+
f
(
x
)
f
(
y
)
)
f
(
x
+
y
)
=
f
(
x
)
+
f
(
y
)
(1+f(x)f(y))f(x+y)=f(x)+f(y)
(
1
+
f
(
x
)
f
(
y
))
f
(
x
+
y
)
=
f
(
x
)
+
f
(
y
)
.
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