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Problems
Contests
National and Regional Contests
PEN Problems
PEN O Problems
42
42
Part of
PEN O Problems
Problems
(1)
O 42
Source:
5/25/2007
Let
N
n
N_{n}
N
n
denote the number of ordered
n
n
n
-tuples of positive integers
(
a
1
,
a
2
,
…
,
a
n
)
(a_{1},a_{2},\ldots,a_{n})
(
a
1
,
a
2
,
…
,
a
n
)
such that
1
/
a
1
+
1
/
a
2
+
…
+
1
/
a
n
=
1.
1/a_{1}+1/a_{2}+\ldots+1/a_{n}=1.
1/
a
1
+
1/
a
2
+
…
+
1/
a
n
=
1.
Determine whether
N
10
N_{10}
N
10
is even or odd.