Let $u_n=\displaystyle\Re\left( \frac{1+i\sqrt{7}}{2}\right)^n$
Prove that $|u_n| \to \infty$
This appeared in a recent issue of French Revue de la Filière Mathématiques, as it was reportedly asked during an oral exam.
The editor deems it is an "extremely difficult problem", and uses Skolem–Mahler–Lech theorem to prove the result.
They're also looking for a proof an undergraduate could find.
Do you know one ?
