The numbers $\displaystyle 9^n\pm\2$ are both primes for n=1 and n=2 in which the pairs are 7, 11 and 79, 83. Prove $\displaystyle 9^n-2$ is composite for infinitely many positive integers n and prove $\displaystyle 9^n+2 $ is composite for infinitely many n.

Note: This my first LaTex post, and I was pretty excited even though it is a simple equation.