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IMC
1999 IMC
3
very well-known
very well-known
Source: IMC 1999 day 2 problem 3
November 19, 2005
real analysis
real analysis unsolved
Problem Statement
Let
x
i
≥
−
1
x_i\ge -1
x
i
≥
−
1
and
∑
i
=
1
n
x
i
3
=
0
\sum^n_{i=1}x_i^3=0
∑
i
=
1
n
x
i
3
=
0
. Prove
∑
i
=
1
n
x
i
≤
n
3
\sum^n_{i=1}x_i \le \frac{n}{3}
∑
i
=
1
n
x
i
≤
3
n
.
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