I am given $$
F\_n = \frac{\varphi^n - \psi^n}{\sqrt{5}}
$$
where, $\varphi = \frac{1 + \sqrt{5}}{2}$ and $\psi = \frac{1 - \sqrt{5}}{2}$.

The textbook states that it's equal to the $n$-th Fibonacci number $F\_n$.
it is stated that since the Fibonacci numbers are integers, the number in $$
F\_n = \frac{\varphi^n - \psi^n}{\sqrt{5}}
$$
is an integer as well. can you guys clarify this please?

> 
> How do I go on proving that the number
>  $$F\_n = \frac{\varphi^n - \psi^n}{\sqrt{5}}$$
>  is an integer using Newton's Binomial Theorem? 
> 
> 
>