Math induction problem with large numbers I am trying to figure out how to prove $17^{200} - 1$ is a multiple of $10$. I am talking simple algebra stuff once everything is set in place.
I have to use mathematical induction.
I figure I need to split $17^{200}$ into something like $(17^{40})^5 - 1$ and have it as $n = 17^{40}$ and $n^5 - 1$.
I just don't know if that's a good way to start.

$17^{200} - 1$ is clearly even and so it remains to prove that it is a multiple of $5$.
Now, $17^{200}= (15+2)^{200}=15a+2^{200}$. So it suffices to prove that $2^{200}-1$ is a multiple of $5$.
Indeed, $2^{200}=(2^{4})^{50}=16^{50}=(5b+1)^{50}=5c+1$.
