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35
P 35
P 35
Source:
May 25, 2007
Additive Number Theory
Problem Statement
Prove that every positive integer which is not a member of the infinite set below is equal to the sum of two or more distinct numbers of the set
{
3
,
−
2
,
2
2
3
,
−
2
3
,
⋯
,
2
2
k
3
,
−
2
2
k
+
1
,
⋯
}
=
{
3
,
−
2
,
12
,
−
8
,
48
,
−
32
,
192
,
⋯
}
.
\{ 3,-2, 2^{2}3,-2^{3}, \cdots, 2^{2k}3,-2^{2k+1}, \cdots \}=\{3,-2, 12,-8, 48,-32, 192, \cdots \}.
{
3
,
−
2
,
2
2
3
,
−
2
3
,
⋯
,
2
2
k
3
,
−
2
2
k
+
1
,
⋯
}
=
{
3
,
−
2
,
12
,
−
8
,
48
,
−
32
,
192
,
⋯
}
.
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