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Putnam
1997 Putnam
5
Putnam 1997 A5
Putnam 1997 A5
Source:
May 30, 2014
Putnam
college contests
Problem Statement
Let
N
k
N_k
N
k
denote number of ordered
n
n
n
-tuples of positive integers
(
a
1
,
a
2
,
⋯
,
a
k
)
(a_1,a_2, \cdots ,a_k)
(
a
1
,
a
2
,
⋯
,
a
k
)
such that
1
a
1
+
1
a
2
+
…
+
1
a
k
=
1
\frac{1}{a_1}+\frac{1}{a_2}+\ldots +\frac{1}{a_k}=1
a
1
1
+
a
2
1
+
…
+
a
k
1
=
1
Determine
N
10
N_{10}
N
10
is odd or even.
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