Not entirely sure if this is where I should post, but I need help.
I need to prove $7\mid (9^n - 2^n)$ for all $n\ge 1$. I have the parts for $n = 1$. But when it comes to solving $k \implies k+1$, I run into issues.
I get that $(9^k - 2^k) = 7a$. But here $(9\cdot 9^k - 2\cdot 2^k)$ is where I have trouble factoring out a $7$.
Any help would be appreciated.