Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
5772618 | Journal of Number Theory | 2017 | 17 Pages |
Abstract
In 1975, Michael Szalay showed that for any prime p>1019 and any integer δ with 1â¤Î´â¤pâ1, there exist at least two primitive roots g and h modulo p such that gâhâ¡Î´(modp). Very recently, Brazelton, Harrington, Kannan and Litman have shown that for any n>6, there exists a prime pâ¡1(modn) for which there are two elements a and b of order n modulo p such that aâbâ¡1(modp). In this article, we extend these ideas to investigate arbitrary differences δ between elements of the same arbitrary order n modulo a prime pâ¡1(modn). Moreover, we show how all elements of a specific order n can be derived from a single fixed difference δ. Finally, we deduce a result concerning the differences between primitive roots for certain primes pâ¡3(mod4).
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
Joshua Harrington, Lenny Jones,