Hint to prove that $\phi^n + \phi'^n$ is an integer. – math.stackexchange.com

Hint to prove that $\phi^n + \phi'^n$ is an integer. – math.stackexchange.com

I was solving some induction exercises but I found this that I could not
solve. Let $n \in \mathbb{N}$, prove that $\phi^n + \phi'^n$ is an integer
where $\phi=\frac{1+\sqrt{5}}{2}$ and ...