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Iran MO (3rd Round)
2001 Iran MO (3rd Round)
1
1
Part of
2001 Iran MO (3rd Round)
Problems
(1)
Rational Functional Equation
Source: Iran National Olympiad (3rd Round) 2001
7/13/2007
Find all functions
f
:
Q
⟶
Q
f: \mathbb Q\longrightarrow\mathbb Q
f
:
Q
⟶
Q
such that:
f
(
x
)
+
f
(
1
x
)
=
1
f(x)+f(\frac1x)=1
f
(
x
)
+
f
(
x
1
)
=
1
2
f
(
f
(
x
)
)
=
f
(
2
x
)
2f(f(x))=f(2x)
2
f
(
f
(
x
))
=
f
(
2
x
)
function
induction
number theory proposed
number theory
functional equation