Proof of factor by induction

Question

Prove by mathematical induction that $4$ is a factor of $9^n - 5^n\,\forall n\geq1$.

Please have a look at my attempt if it is correct or not.

Answer 1

Everything is ok, except the last line where you used $ 4(9k+5^n) = 4n.$

As you notice, n is used to mean two different things.

Change the last $4n$ to $4m$ and you have a good proof.