Re: [math-fun] Characterizing polys which permute GF(p)

We also have a theorem by Fryer (195?): The permutations in GF(p) x->x+1 and x->m*x^(p-2) [i.e., x->m/x] generate the full symmetric group when p=4n+1 and m is a square, or p=4n+3 and m is a non-square. and generate the alternating group when p=4n+1 and m is a nonsquare, or p=4n+3 and m is a square. Fryer, K.D. "Note on permutations in a finite field". AMS 195?