Chebolu, Sunil K.; Lockridge, Keir; Yamskulna, Gaywalee Characterizations of Mersenne and 2-rooted primes. (English) Zbl 1343.11005 Finite Fields Appl. 35, 330-351 (2015). 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. Cited in 4 Documents MSC: 11A41 Primes 11A07 Congruences; primitive roots; residue systems 15B99 Special matrices 05C90 Applications of graph theory Keywords:Mersenne primes; group algebras; circulant matrices; primitive roots; bipartite graphs PDFBibTeX XMLCite \textit{S. K. Chebolu} et al., Finite Fields Appl. 35, 330--351 (2015; Zbl 1343.11005) Full Text: DOI arXiv References: [1] Aulicino, D. J.; Goldfeld, M., A new relation between primitive roots and permutations, Am. Math. Mon., 76, 664-666 (1969) · Zbl 0239.10003 [2] Bollobas, B., Modern Graph Theory, Graduate Texts in Mathematics, vol. 184 (1998), Springer-Verlag: Springer-Verlag New York, xiv+394 pp · Zbl 0902.05016 [3] Burton, D., Elementary Number Theory (1989), W.C. Brown Publishers: W.C. Brown Publishers Dubuque, IA, xviii+450 pp [4] Chebolu, S. K., What is special about the divisors of 24?, Math. Mag., 85, 5 (2012) · Zbl 1274.97016 [5] Chebolu, S. K.; Mayers, M., What is special about the divisors of 12?, Math. Mag., 86, 2 (2013) · Zbl 1293.97015 [6] Dolan, D., Group of units in a finite ring, J. Pure Appl. Algebra, 170, 2-3, 175-183 (2002) [7] Dummit, D. S.; Foote, R. M., Abstract Algebra (2004), John Wiley & Sons, Inc.: John Wiley & Sons, Inc. Hoboken, NJ, xii+932 pp · Zbl 1037.00003 [9] Hooley, C., On Artin’s conjecture, J. Reine Angew. Math., 225, 209-220 (1967) · Zbl 0221.10048 [10] Kosher, T., Elementary Number Theory with Applications (2007), Academic Press [11] Gupta, R.; Murty, M. R., A remark on Artin’s conjecture, Invent. Math., 78, 1, 127-130 (1984) · Zbl 0549.10037 [12] Lovasz, L.; Plummer, M. D., Matching Theory, North-Holland Mathematics Studies. North-Holland Mathematics Studies, Annals of Discrete Mathematics, vol. 29 (1986), North-Holland Publishing Co.: North-Holland Publishing Co. Amsterdam: Publishing House of the Hungarian Academy of Sciences: North-Holland Publishing Co.: North-Holland Publishing Co. Amsterdam: Publishing House of the Hungarian Academy of Sciences Budapest, xxvii+544 pp · Zbl 0618.05001 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.