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Vojtěch Jarník IMC
2017 VJIMC
1
Functional equation with continuity implies constant
Functional equation with continuity implies constant
Source: VJIMC 2017, Category I, Problem 1
April 2, 2017
Problem Statement
Let
f
:
R
→
R
f:\mathbb{R} \to \mathbb{R}
f
:
R
→
R
be a continuous function satisfying
f
(
x
+
2
y
)
=
2
f
(
x
)
f
(
y
)
f(x+2y)=2f(x)f(y)
f
(
x
+
2
y
)
=
2
f
(
x
)
f
(
y
)
for every
x
,
y
∈
R
x,y \in \mathbb{R}
x
,
y
∈
R
. Prove that
f
f
f
is constant.
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