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TOT 161 1987 Autumn S5 colouring pairs of integers

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April 19, 2020
ColoringcombinatoricsInteger

Problem Statement

Consider the set of all pairs of positive integers (A,B)(A , B) in which A<BA < B . Some of these pairs are to bebe designated as "black" , while the remainder are to be designated as "white" . Is it possible to designate these pairs in such a way that for any triple of positive integers of form A,A+D,A+2DA, A + D, A + 2D, in which D>0D > 0, the associated pairs (A,A+D)(A, A + D ) , (A,A+2D)(A , A + 2D) and (A+D,A+2D)(A + D, A + 2D) would include at least one pair of each colour?
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