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Problems
Contests
National and Regional Contests
Argentina Contests
Argentina National Olympiad
2010 Argentina National Olympiad
4
4
Part of
2010 Argentina National Olympiad
Problems
(1)
sum of all products a_1a_2...a_{50}
Source: 2010 Argentina OMA Finals L3 p4
1/15/2023
Find the sum of all products
a
1
a
2
.
.
.
a
50
a_1a_2...a_{50}
a
1
a
2
...
a
50
, where
a
1
,
a
2
,
.
.
.
,
a
50
a_1,a_2,...,a_{50}
a
1
,
a
2
,
...
,
a
50
are distinct positive integers, less than or equal to
101
101
101
, and such that no two of them add up to
101
101
101
.
algebra
Sum