Characterizations of Mersenne and 2-rooted primes

descriptionPublicationkeyboard_double_arrow_right Article , Preprint 01 Sep 2015Embargo end date: 01 Jan 2014 English Publisher:Elsevier BVJournal:Finite Fields and Their Applications, volume 35, pages 330-351 (issn: 1071-5797,

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Authors: Sunil K. Chebolu; Keir Lockridge; Gaywalee Yamskulna;

doi: 10.1016/j.ffa.2015.06.003 , 10.48550/arxiv.1404.4096

arXiv: 1404.4096

Characterizations of Mersenne and 2-rooted primes

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Abstract

We give several characterizations of Mersenne primes (Theorem 1.1) and of primes for which 2 is a primitive root (Theorem 1.2). These characterizations involve group algebras, circulant matrices, binomial coefficients, and bipartite graphs.

19 pages, final version, to appear in Finite Fields and their Applications

Related Organizations

Gettysburg College
United States
Illinois State University
United States

Keywords

primitive roots, group algebras, bipartite graphs, Mathematics - Number Theory, Applications of graph theory, Mersenne primes, Special matrices, Primes, Primary 11A41, 11A07, Secondary 15B99, 05C90, FOS: Mathematics, Mathematics - Combinatorics, Congruences; primitive roots; residue systems, Number Theory (math.NT), Combinatorics (math.CO), circulant matrices

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