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Parition of set into arithmetic progressions

Source: 44th International Tournament of Towns, Junior A-Level P6, Spring 2023

January 9, 2024
number theoryArithmetic Progression

Problem Statement

Let XX{} be a set of integers which can be partitioned into NN{} disjoint increasing arithmetic progressions (infinite in both directions), and cannot be partitioned into a smaller number of such progressions. Is such partition into NN{} progressions unique for every such XX{} if a) N=2N = 2{} and b) N=3N = 3?
Viktor Kleptsyn
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