How do I show that $\displaystyle 2^{1996} \equiv 1 (mod $ $\displaystyle 1997)$ 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

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- Nov 17th 2009, 07:24 PMezongprimitive root question
How do I show that $\displaystyle 2^{1996} \equiv 1 (mod $ $\displaystyle 1997)$ 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 - Nov 17th 2009, 07:33 PMaman_cc
Can't you use Fermat's Little Theorem?

Fermat's little theorem - Wikipedia, the free encyclopedia