Characterizations of Mersenne and 2-rooted primes
  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. 
Sunil K. Chebolu, Keir Lockridge, and Gaywalee Yamskulna
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