Permutation Polynomials Modulo 2w

We give an exact characterization of permutation polynomials modulo n=2w, w≥2: a polynomial P(x)=a0+a1x +•••+adxd with integral coefficients is a permutation polynomial modulo n if and only if a1 is odd, (a2+a4+a6+•••) is even, and (a3+a5+a7+•••) is even. We also characterize polynomials defining latin squares modulo n=2w, but prove that polynomial multipermutations (that is, a pair of polynomials defining a pair of orthogonal latin squares) modulo n=2wdo not exist.