Bulletin of the Australian Mathematical Society

Table of Contents - June 2012 - Volume 85, Issue 03  

Research Article

SUM–PRODUCT ESTIMATES AND MULTIPLICATIVE ORDERS OF γ AND γ+γ−1 IN FINITE FIELDS

IGOR SHPARLINSKIa1

a1 Department of Computing, Macquarie University, NSW 2109, Australia (email: igor.shparlinski@mq.edu.au)

Abstract

Using a recent result on the sum–product problem, we estimate the number of elements γ in a prime finite field such that both γ and γ+γ−1 are of small order.

(Received September 01 2011)

2010 Mathematics subject classification

  • primary 11T30; secondary 11B30

Keywords and phrases

  • multiplicative order;
  • sum–product theorem