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x+y cannot be divisible by x-y

Source: Romanian IMO Team Selection Test TST 1987, problem 3

September 25, 2005
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Problem Statement

Let AA be the set A={1,2,…,n}A = \{ 1,2, \ldots, n\}. Determine the maximum number of elements of a subset B⊂AB\subset A such that for all elements x,yx,y from BB, x+yx+y cannot be divisible by x−yx-y. Mircea Lascu, Dorel Mihet
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