Nonexistence of Permutation Binomials of Certain Shapes - Masuda, Ariane M.; Zieve, Michael E. (The Electronic Journal of Combinatorics, 2007)
Suppose x^m+ax^n is a permutation polynomial over F_p, where p>5 is prime and m>n>0 and aF_p^*. We prove that (m-n,p-1) otin{2,4}. In the special case that either (p-1)/2 or (p-1)/4 is prime, this was conjectured in a recent paper by Masuda, Panario and Wang.