Permutation binomials over finite fields
Abstract
We prove that if xm + c*xn permutes the prime field GF(p), where m>n>0 and c is in GF(p)*, then gcd(m-n,p-1) > sqrtp - 1. Conversely, we prove that if q>=4 and m>n>0 are fixed and satisfy gcd(m-n,q-1) > 2q*(log log q)/(log q), then there exist permutation binomials over GF(q) of the form xm + c*xn if and only if gcd(m,n,q-1) = 1.
0
Turn this paper into a lesson
ArcXiv compiles a structured reading guide from this paper's metadata: plain-English importance, contributions, prerequisite concepts, which sections to read first, flashcards, and a quiz. Grounded in the abstract, never invented.