Lehmer's equations in new domains
Abstract
In this paper, we examine the equations kφG(β) = q(β)±1 and kφG(β) = q(β) in the domains of Gaussian integersZ[i] and the polynomial rings over finite fieldsZp[x], where p is prime inZ. Properties concerning the existence of solutions are studied. Complete characterization for the solutions of the above equations is given in the two domains.
Copyright © 2014 Haissam Y. Chehade. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Cite this article
H. Y. Chehade, Lehmer's equations in new domains, J. Math. Comput. Sci. 4 (2014), 25–34.
BibTeX
@article{Chehade2014,
author = {Chehade, Haissam Y.},
title = {Lehmer's equations in new domains},
journal = {J. Math. Comput. Sci.},
volume = {4},
year = {2014},
pages = {25--34},
doi = {}
}