BALKAN-SL 2007 A4
Show that the sequence \begin{align*} a_n = \left \lfloor \left( \sqrt[3]{n-2} + \sqrt[3]{n+3} \right)^3 \right \rfloor \end{align*} contains infinitely many terms of the form
Dataset text AI-MO AoPS. Quoted with source.
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