show by induction that $4^{2n+1}+3^{n+2}$ is divisible by $13$

Question

i'm stuck in this problem, anyone can give me a hint, please?

"Show by induction that $4^{2n+1} + 3^{n+2}$ is divisible by $13$

In my attempt i got the expression

$$4^{2}\cdot 4^{2n+1} + 3\cdot 3^{n+2}$$

but i can't go more, any suggestion is thankful.

Answer 1

\begin{eqnarray*} 4^{2}\cdot 4^{2n+1} + 3\cdot 3^{n+2}= 16(4^{2n+1}+3^{n+2}) -13 \times 3^{n+2}. \end{eqnarray*}