I am trying to find n such that $\displaystyle 3^{n} + 2^{n}$ is divisible by 13.

I am trying to let $\displaystyle n = 12x + r$ and $\displaystyle n = 12y + s$ which gives $\displaystyle 3^{12x + r} + 2^{12y + s}$. But I end up running in circles and getting nowhere!

Any ideas?