IMO Shortlist 1989 problem 9


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2. travnja 2012.
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\forall n > 0, n \in \mathbb{Z}, there exists uniquely determined integers a_n, b_n, c_n \in \mathbb{Z} such

\left(1 + 4 \cdot \sqrt[3]{2} - 4 \cdot \sqrt[3]{4} \right)^n = a_n + b_n \cdot \sqrt[3]{2} + c_n \cdot \sqrt[3]{4}.

Prove that c_n = 0 implies n = 0.
Izvor: Međunarodna matematička olimpijada, shortlist 1989