Mathematical induction proving positive integers

Question

Prove that if $n$ is a positive integer, then $7^n-1$ is a multiple of $6$.

Answer 1

I think you meant this $$7^n-1$$ is divisible by $6$

This can be factored like this $$(7-1)(7^{n-1}+7^{n-2}+...+1)$$ which is obviously divisible by $6$.