MathDB

2008 KMO P4

Source:

August 9, 2015

combinatoricsnumber theory

Problem Statement

We define

A, B, C

as a partition of

\mathbb{N}

if

A,B,C

satisfies the following. (i)

A, B, C \not= \phi

(ii)

A \cap B = B \cap C = C \cap A = \phi

(iii)

A \cup B \cup C = \mathbb{N}

.
Prove that the partition of

\mathbb{N}

satisfying the following does not exist. (i)

\forall

a \in A, b \in B

, we have

a+b+2008 \in C

(ii)

\forall

b \in B, c \in C

, we have

b+c+2008 \in A

(iii)

\forall

c \in C, a \in A

, we have

c+a+2008 \in B

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