Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
5772720 | Journal of Number Theory | 2017 | 12 Pages |
Abstract
Given nâN, we study the conditions under which a finite field of prime order q will have adjacent elements of multiplicative order n. In particular, we analyze the resultant of the cyclotomic polynomial Φn(x) with Φn(x+1), and exhibit Lucas and Mersenne divisors of this quantity. For each nâ 1,2,3,6, we prove the existence of a prime qn for which there is an element αâZqn where α and α+1 both have multiplicative order n. Additionally, we use algebraic norms to set analytic upper bounds on the size and quantity of these primes.
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
Thomas Brazelton, Joshua Harrington, Siddarth Kannan, Matthew Litman,