The sequence contains infinitely many terms of the given form
Source: Balkan MO ShortList 2007 A4
April 6, 2020
Problem Statement
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