Can you divide this by $7$ without a remainder ? $ 13^{101}-13^{95} $

Question

Just need some help with basic math. How do i know if i can divide this expression by $7$ without a remainder ?

$ 13^{101}-13^{95} $

Answer 1

Hint: A number $n$ is divisible by $7$ if and only if $n\equiv 0\pmod{7}$. Note that $13 \equiv 2\cdot 7 - 1\equiv -1\pmod{7}$.

Answer 2

Fermat's little theorem is sufficient : Note $13^{101}-13^{95}=13^{95}\cdot (13^6-1)$

Since $7$ is a prime not dividing $13$, we have $7|13^6-1$ because of Fermat's little theorem.