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Partition of Natural Numbers

Source: IMS 2006

July 13, 2006

inductionnumber theory proposednumber theory

Problem Statement

For each subset

C

of

\mathbb N

, Suppose

C\oplus C=\{x+y|x,y\in C, x\neq y\}

. Prove that there exist a unique partition of

\mathbb N

to sets

A

,

B

that

A\oplus A

and

B\oplus B

do not have any prime numbers.

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