MathDB
Problems
Contests
National and Regional Contests
Argentina Contests
Argentina Team Selection Test
2009 Argentina Team Selection Test
2
2
Part of
2009 Argentina Team Selection Test
Problems
(1)
Find the maximum value
Source: Argentina TST 2009
5/15/2009
Let
a
1
,
a
2
,
.
.
.
,
a
300
a_1, a_2, ..., a_{300}
a
1
,
a
2
,
...
,
a
300
be nonnegative real numbers, with \sum_{i\equal{}1}^{300} a_i \equal{} 1. Find the maximum possible value of
∑
i
≠
j
,
i
∣
j
a
i
a
j
\sum_{i \neq j, i|j} a_ia_j
∑
i
=
j
,
i
∣
j
a
i
a
j
.
inequalities
Clevermath