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a, b, a + b either all belong to A or all belong to B where A,B partitions of N

Source: Austrian Polish 1983 APMC

April 30, 2020
number theorypositive integersSetspartition

Problem Statement

The set NN has been partitioned into two sets A and BB. Show that for every nāˆˆNn \in N there exist distinct integers a,b>na, b > n such that a,b,a+ba, b, a + b either all belong to AA or all belong to BB.
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