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Characterizations of Mersenne and 2-rooted primes. (English) Zbl 1343.11005

Summary: 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.

MSC:

11A41 Primes
11A07 Congruences; primitive roots; residue systems
15B99 Special matrices
05C90 Applications of graph theory
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