<s>[INST] Let $q \in \mathbb{Q}$ and $f_n = (2 + \sqrt{3})^n + (2 - \sqrt{3})^n$. Show that $f_n$ is always an even integer.
$f_1 = 2 + \sqrt{3} + 2 - \sqrt{3} = 4$, an integer. $f_2 = 7 + 2 \sqrt{3} + 7 - 2 \sqrt{3} = 14$, an integer, $f_3= 26 + 6 \sqrt{3} + 26 - 6 \sqrt{3} = 52$, an integer. How do we prove that this works for all n?[/INST]