IMO Shortlist 1999 problem A4


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2. travnja 2012.
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Prove that the set of positive integers cannot be partitioned into three nonempty subsets such that, for any two integers x,y taken from two different subsets, the number x^2-xy+y^2 belongs to the third subset.
Izvor: Međunarodna matematička olimpijada, shortlist 1999