Nonexistence of Permutation Binomials of Certain Shapes

Suppose xm + axn is a permutation polynomial over Fp, where p > 5 is prime and m > n > 0 and a ∈ F∗ p. 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.

• Type: Journal
• Year: 2007
• Where: COMBINATORICS
• Authors: Ariane M. Masuda, Michael E. Zieve
• Keywords: COMBINATORICS 2007, Masuda, Permutation Polynomial, Special Case