MEMO 2011 ekipno problem 7


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28. travnja 2012.
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Let A and B be disjoint nonempty sets with A \cup  B = \{1, 2,3, \ldots, 10\}. Show that there exist elements a \in A and b \in B such that the number a^3 + ab^2 + b^3 is divisible by 11.
Izvor: Srednjoeuropska matematička olimpijada 2011, ekipno natjecanje, problem 7