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National and Regional Contests
Cuba Contests
Cuba MO
2005 Cuba MO
6
6
Part of
2005 Cuba MO
Problems
(1)
|a_i -a_j| all different
Source: 2005 Cuba MO 2.6
9/15/2024
All positive differences
a
i
−
a
j
a_i -a_j
a
i
−
a
j
of five different positive integers
a
1
a_1
a
1
,
a
2
a_2
a
2
,
a
3
a_3
a
3
,
a
4
a_4
a
4
and
a
5
a_5
a
5
are all different. Let
A
A
A
be the set formed by the largest elements of each group of
5
5
5
elements that meet said condition. Determine the minimum element of
A
A
A
.
algebra
inequalities