IMO Shortlist 2012 problem N1


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3. studenoga 2013.
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Call admissible a set A of integers that has the following property:
If x,y \in A (possibly x=y) then x^2+kxy+y^2 \in A for every integer k.
Determine all pairs m,n of nonzero integers such that the only admissible set containing both m and n is the set of all integers.

Proposed by Warut Suksompong, Thailand
Izvor: Međunarodna matematička olimpijada, shortlist 2012