Characterizations of Mersenne and 2-rooted primes
Sunil K. Chebolu, Keir Lockridge, and Gaywalee Yamskulna
TL;DR
This paper provides new characterizations of Mersenne primes and primes with 2 as a primitive root using algebraic and combinatorial tools.
Contribution
It introduces novel characterizations involving group algebras, circulant matrices, binomial coefficients, and bipartite graphs.
Findings
Characterizations of Mersenne primes
Characterizations of primes with 2 as a primitive root
Connections between algebraic structures and prime properties
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.
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Taxonomy
TopicsAdvanced Topics in Algebra · Finite Group Theory Research · Rings, Modules, and Algebras