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Problems
Contests
National and Regional Contests
Poland Contests
Poland - Second Round
2002 Poland - Second Round
1
Periodic
Periodic
Source: Poland
June 11, 2005
function
algebra
Problem Statement
Prove that all functions
f
:
R
→
R
f:\mathbb{R}\rightarrow\mathbb{R}
f
:
R
→
R
satisfying, for all real
x
x
x
,
f
(
x
)
=
f
(
2
x
)
=
f
(
1
−
x
)
f(x)=f(2x)=f(1-x)
f
(
x
)
=
f
(
2
x
)
=
f
(
1
−
x
)
are periodic.
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