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Baltic Way
2016 Baltic Way
8
8
Part of
2016 Baltic Way
Problems
(1)
Functional equation
Source: Baltic Way 2016, Problem 8
11/5/2016
Find all real numbers
a
a
a
for which there exists a non-constant function
f
:
R
→
R
f :\Bbb R \to \Bbb R
f
:
R
→
R
satisfying the following two equations for all
x
∈
R
:
x\in \Bbb R:
x
∈
R
:
i)
f
(
a
x
)
=
a
2
f
(
x
)
f(ax) = a^2f(x)
f
(
a
x
)
=
a
2
f
(
x
)
and ii)
f
(
f
(
x
)
)
=
a
f
(
x
)
.
f(f(x)) = a f(x).
f
(
f
(
x
))
=
a
f
(
x
)
.
algebra
functional equation