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Two-part partition of N

Source: Kürschak 2009, problem 2

July 8, 2014
number theory unsolvednumber theory

Problem Statement

Find all positive integer pairs (a,b)(a,b) for which the set of positive integers can be partitioned into sets H1H_1 and H2H_2 such that neither aa nor bb can be represented as the difference of two numbers in HiH_i for i=1,2i=1,2.
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