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IMS
2006 IMS
2
2
Part of
2006 IMS
Problems
(1)
Partition of Natural Numbers
Source: IMS 2006
7/13/2006
For each subset
C
C
C
of
N
\mathbb N
N
, Suppose
C
⊕
C
=
{
x
+
y
∣
x
,
y
∈
C
,
x
≠
y
}
C\oplus C=\{x+y|x,y\in C, x\neq y\}
C
⊕
C
=
{
x
+
y
∣
x
,
y
∈
C
,
x
=
y
}
. Prove that there exist a unique partition of
N
\mathbb N
N
to sets
A
A
A
,
B
B
B
that
A
⊕
A
A\oplus A
A
⊕
A
and
B
⊕
B
B\oplus B
B
⊕
B
do not have any prime numbers.
induction
number theory proposed
number theory