Fermats little theorem/Talk

Maybe this should be shortend by creating a new lemma 'prime test' or 'probably prime test' or similiar. Does any body know a reference for the strong prime test?

I find the style of the proof a bit colloquial, it should be cleared up.

An alternative proof is the following:

Let S be the set {1,2,.., p-1} multiplication with a mod p induces a permution on S. Hence their products are equal,

1*2*..*(p-1)= (a*1)*(a*2)*...*(a*(p-1)) mod p

Since p is prime, the product 1*2*..*p-1 can be divided out and the result follows.

While we're at it we might as well refer to Lagrange's theorem and be done with it.