IMO Shortlist 2004 problem A3


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2. travnja 2012.
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Does there exist a function s\colon \mathbf{Q} \rightarrow \{-1,1\} such that if x and y are distinct rational numbers satisfying {xy=1} or {x+y\in \{0,1\}}, then {s(x)s(y)=-1}? Justify your answer.
Izvor: Međunarodna matematička olimpijada, shortlist 2004