# Mathematical induction proving positive integers

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

• do you mean $$n^7-1$$ is divisible by $6$? – Dr. Sonnhard Graubner Mar 23 '17 at 7:19
• If he does it's not true. $2^7-1=127$ is not divisible by $6$. Perhaps you mean $7^n-1$. But in that case it's trivial. – Mathematician 42 Mar 23 '17 at 7:24

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 $6$.