ELMO 2011 Problem 5

Let $p>13$ be a prime of the form $2q+1$ , where $q$ is prime. Find the number of ordered pairs of integers $(m,n)$ such that $0\le m<n<p-1$ and $$3^m+(-12)^m\equiv 3^n+(-12)^n\pmod{p}.$$

Alex Zhu.