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Permutation binomials over finite fields
- Source :
- Trans. Amer. Math. Soc. 361 (2009) 4169-4180
- Publication Year :
- 2007
-
Abstract
- We prove that if x^m + c*x^n permutes the prime field GF(p), where m>n>0 and c is in GF(p)^*, then gcd(m-n,p-1) > sqrt{p} - 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 x^m + c*x^n if and only if gcd(m,n,q-1) = 1.<br />Comment: 12 pages; various minor changes
- Subjects :
- Mathematics - Number Theory
11T06
Subjects
Details
- Database :
- arXiv
- Journal :
- Trans. Amer. Math. Soc. 361 (2009) 4169-4180
- Publication Type :
- Report
- Accession number :
- edsarx.0707.1108
- Document Type :
- Working Paper