# Math Help - primitive root question

1. ## primitive root question

How do I show that $2^{1996} \equiv 1 (mod$ $1997)$ given 1996= (2^2)(499)? There's probably an easy way but I'm just not that smart.

I forgot to mention you have to show that 1997 is prime

2. Originally Posted by ezong
How do I show that $2^{1996} \equiv 1 (mod$ $1997)$ given 1996= (2^2)(499)? There's probably an easy way but I'm just not that smart.
Can't you use Fermat's Little Theorem?
Fermat's little theorem - Wikipedia, the free encyclopedia