Nonexistence of permutation binomials of certain shapes

Abstract

Suppose xm + axn is a permutation polynomial over double struk D signp, where p > 5 is prime and m > n > 0 and a ∈ double struk D signp*. We prove that gcd(m - n, p - 1) ∉ {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.