MathDB

A4

Part of 2007 Balkan MO Shortlist

Problems(1)

The sequence contains infinitely many terms of the given form

Source: Balkan MO ShortList 2007 A4

4/6/2020
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 anana_n^{a_n}