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2013 China Northern MO
2
China Northern Mathematical Olympiad 2013 , Problem 2
China Northern Mathematical Olympiad 2013 , Problem 2
Source: China Xian 27 Jul 2013
August 26, 2013
inequalities
inequalities proposed
algebra
Problem Statement
If
a
1
,
a
2
,
⋯
,
a
2013
∈
[
−
2
,
2
]
a_1,a_2,\cdots,a_{2013}\in[-2,2]
a
1
,
a
2
,
⋯
,
a
2013
∈
[
−
2
,
2
]
and
a
1
+
a
2
+
⋯
+
a
2013
=
0
a_1+a_2+\cdots+a_{2013}=0
a
1
+
a
2
+
⋯
+
a
2013
=
0
, find the maximum of
a
1
3
+
a
2
3
+
⋯
+
a
2013
3
a^3_1+a^3_2+\cdots+a^3_{2013}
a
1
3
+
a
2
3
+
⋯
+
a
2013
3
.
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