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Putnam
1954 Putnam
B6
B6
Part of
1954 Putnam
Problems
(1)
Problem about there exits
Source:
8/11/2012
Let
x
∈
Q
+
x \in \mathbb{Q}^+
x
∈
Q
+
. Prove that there exits
α
1
,
α
2
,
.
.
.
,
α
k
∈
N
\alpha_1,\alpha_2,...,\alpha_k \in \mathbb{N}
α
1
,
α
2
,
...
,
α
k
∈
N
and pairwe distinct such that
x
=
∑
i
=
1
k
1
α
i
x= \sum_{i=1}^{k} \frac{1}{\alpha_i}
x
=
i
=
1
∑
k
α
i
1
algorithm
number theory unsolved
number theory