Mathmatical Induction Prove, by mathmatical induction, that $5^{2n}$ + $2^{2n-2}$$3^{n-1}$ is divisible by $13$.
I first plugged in n as 1 and showed that the expression is divisible by 13 for n=1. 
Then I assumed that the expression was divisible by 13 for n=k and plugged in k. The simplified expression in terms of k was $25^k$ + $\frac{4^n3^n}{12}$. I then plugged in k+1 and got an expression for that. I am unable to show that the sum or difference of the k and k+1 expressions is divisible by 13. How do I proceed?

$$25^{k+1}+\frac{4^{k+1}3^{k+1}}{12}=25\cdot 25^{k}+12 \frac{4^{k}3^{k}}{12} $$
$$=13\cdot 25^k+12\cdot25^k+12 \frac{4^{k}3^{k}}{12} $$
$$=13\cdot 25^k + 12 \left(25^k+ \frac{4^{k}3^{k}}{12}\right)$$
