Nonexistence of permutation binomials of certain shapes
Abstract
Suppose xm + c*xn is a permutation polynomial over GF(p), where p>5 is prime, m>n>0, and c is in GF(p)*. We prove that gcd(m-n,p-1) is not 2 or 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.
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