- Prove, using induction, that $ 7^n - 1 $ is always divisible by $6$, as long as $n$ is an integer.
Another way of writing that that expression is divisible by $6$ is to say that $ 7^n - 1 = 6x$, where $x$ is some integer. ($x$ is the whole number you would get if you divided $7^n -1$ by $6$.