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

This is a very cool theorem: Supposedly (I don't have access to this paper), [Carlitz1953] proved for any finite field GF(q=p^n), q>2, the whole symmetric group is generated by the power map x->x^(q-2) and the linear polynomials over GF(q). Notice that this map takes any non-zero field element to its inverse, and hence is an involution. Carlitz, L. "Permutations on a finite field". Proc. Amer. Math. Soc. 4 (1953), 538.