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Putnam
2005 Putnam
B2
B2
Part of
2005 Putnam
Problems
(1)
Putnam 2005 B2
Source:
12/5/2005
Find all positive integers
n
,
k
1
,
…
,
k
n
n,k_1,\dots,k_n
n
,
k
1
,
…
,
k
n
such that
k
1
+
⋯
+
k
n
=
5
n
−
4
k_1+\cdots+k_n=5n-4
k
1
+
⋯
+
k
n
=
5
n
−
4
and
1
k
1
+
⋯
+
1
k
n
=
1.
\frac1{k_1}+\cdots+\frac1{k_n}=1.
k
1
1
+
⋯
+
k
n
1
=
1.
Putnam
inequalities
college contests