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IMO Longlists
1986 IMO Longlists
45
45
Part of
1986 IMO Longlists
Problems
(1)
IMO Long List 1986 with n variables
Source:
8/29/2010
Given
n
n
n
real numbers
a
1
≤
a
2
≤
⋯
≤
a
n
a_1 \leq a_2 \leq \cdots \leq a_n
a
1
≤
a
2
≤
⋯
≤
a
n
, define M_1=\frac 1n \sum_{i=1}^{n} a_i , M_2=\frac{2}{n(n-1)} \sum_{1 \leq i
a
1
≤
M
1
−
Q
≤
M
1
+
Q
≤
a
n
a_1 \leq M_1 - Q \leq M_1 + Q \leq a_n
a
1
≤
M
1
−
Q
≤
M
1
+
Q
≤
a
n
and that equality holds if and only if
a
1
=
a
2
=
⋯
=
a
n
.
a_1 = a_2 = \cdots = a_n.
a
1
=
a
2
=
⋯
=
a
n
.
inequalities
inequalities proposed