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ij divides x_i+x_j for any distinct positive integer i,j (HOMC 2007 Q7)

Source:

July 23, 2019
number theorySequence

Problem Statement

Find all sequences of integer x1,x2,..,xn,...x_1,x_2,..,x_n,... such that ijij divides xi+xjx_i+x_j for any distinct positive integer ii, jj.
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