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Paritioning positive integers into A and B with conditions

Source: Baltic Way 1996 Q20

February 22, 2005

arithmetic sequencecombinatorics unsolvedcombinatorics

Problem Statement

Is it possible to partition all positive integers into disjoint sets

A

and

B

such that (i) no three numbers of

A

form an arithmetic progression, (ii) no infinite non-constant arithmetic progression can be formed by numbers of

B