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Problems
Contests
National and Regional Contests
PEN Problems
PEN O Problems
34
34
Part of
PEN O Problems
Problems
(1)
O 34
Source:
5/25/2007
Determine for which positive integers
k
k
k
, the set
X
=
{
1990
,
1990
+
1
,
1990
+
2
,
⋯
,
1990
+
k
}
X=\{1990, 1990+1, 1990+2, \cdots, 1990+k \}
X
=
{
1990
,
1990
+
1
,
1990
+
2
,
⋯
,
1990
+
k
}
can be partitioned into two disjoint subsets
A
A
A
and
B
B
B
such that the sum of the elements of
A
A
A
is equal to the sum of the elements of
B
B
B
.