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National and Regional Contests
Romania Contests
Romania National Olympiad
1996 Romania National Olympiad
1996 Romania National Olympiad
Part of
Romania National Olympiad
Subcontests
(5)
1
4
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2
5
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2a
1
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very nice
Suppose that
f
1
,
f
2
,
.
.
.
,
f
n
:
R
→
R
f_1,f_2,...,f_n: \mathbb{R}\rightarrow \mathbb{R}
f
1
,
f
2
,
...
,
f
n
:
R
→
R
are the periodic functions and
f
=
f
1
+
f
2
+
.
.
.
+
f
n
,
f
:
R
→
R
f=f_1+f_2+...+f_n , f:\mathbb{R} \rightarrow \mathbb{R}
f
=
f
1
+
f
2
+
...
+
f
n
,
f
:
R
→
R
has an finite limit in
+
∞
+\infty
+
∞
. Prove that
f
f
f
is the constant function.
4
4
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3
4
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