Mathematical Induction and Divisibility $7\mid 11^n-4^n$ Prove $11^{n} - 4^{n}$ is divisible by 7 for all natural numbers n.
I know this holds for the base case of n = 1. Am I supposed to use $11^{n + 1} - 4^{n + 1}$ for the induction step?
Any help would be greatly appreciated!
Thank you in advance!

Another way to to do it without induction is to note that the mod cycles for powers of $11$ and $4$ modulo congruent to $7$ correspond to each other. 
$$\begin{equation}\begin{aligned}11 &\equiv 4 \pmod 7\\ 11^2 &\equiv 2 \pmod 7\\ 11^3 &\equiv 1 \pmod 7 \\ 11^4 &\equiv 4 \pmod 7 \\ &\vdots\end{aligned}\end{equation}$$
$$\begin{equation}\begin{aligned}4 &\equiv 4 \pmod 7\\ 4^2 &\equiv 2 \pmod 7\\ 4^3 &\equiv 1 \pmod 7 \\ 4^4 &\equiv 4 \pmod 7 \\ &\vdots\end{aligned}\end{equation}$$
So for any $n$, $11^n \equiv 4^n \equiv r \pmod 7$, so $11^n - 4^n \equiv r - r \pmod 7 \implies 11^n - 4^n \equiv 0 \pmod 7$ as desired. 
