Number of Integer Solutions to $k^2-2016=3^n$ How many pairs of integers (k,n) satisfy the equation 
$k^2-2016=3^n$
The only thing I could think to do was factor out 3^2 from the entire equation to get
$(k/3)^2-224=3^{n-2}$
but that doesn't lead to anything useful. I know that (45, 2) is a solution, but that was from trial and error. Can you show me how to solve this or at least point me in the right direction? Thanks.

After your simplification, observe that $\frac{k}{3}\equiv 0\text{ or }1$ (mod $3$) and $-224\equiv 1$ (mod $3$). So the right side cannot be divisible by $3$ which gives you $n-2=0$ from where you get $n=2$
