# primitive root question

• November 17th 2009, 07:24 PM
ezong
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.(Doh)

I forgot to mention you have to show that 1997 is prime
• November 17th 2009, 07:33 PM
aman_cc
Quote:

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.(Doh)

Can't you use Fermat's Little Theorem?
Fermat's little theorem - Wikipedia, the free encyclopedia