PERMUTATION BINOMIALS OVER FINITE FIELDS

被引：37
|
作者：
Masuda, Ariane M. [1 ]
Zieve, Michael E. [2 ]
机构：
[1] Carleton Univ, Sch Math & Stat, Ottawa, ON K1S 5B6, Canada
[2] Ctr Commun Res, Princeton, NJ 08540 USA
来源：
TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY | 2009年 / 361卷 / 08期
关键词：
Permutation polynomial; finite field; Weil bound; POLYNOMIALS; NUMBER;
D O I：
10.1090/S0002-9947-09-04578-4
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We prove that if x(m) + ax(n) permutes the prime field F(p), where m > n > 0 and a is an element of F(p)*, then gcd(m - n,p - 1) > root 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 F(q) of the form x(m) + ax(n) if and only if gcd(m, n, q - 1) = 1.
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页码：4169 / 4180
页数：12
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