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17 necessary and sufficient conditions for the primality of Fermat numbers. (English) Zbl 1227.11029
From the text: We give a survey of necessary and sufficient conditions on the primality of the Fermat number $$F_m = 2^{2^m} + 1$$. Some new connections with graph theory are presented. In Theorems 1–3, we introduce three sets of necessary and sufficient conditions for Fermat primes. Most of them are proved in the book of the authors and F. Luca [17 lectures on Fermat numbers. From number theory to geometry. New York, NY: Springer (2001; Zbl 1010.11002)].
##### MSC:
 11A51 Factorization; primality 11A07 Congruences; primitive roots; residue systems 05C20 Directed graphs (digraphs), tournaments
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##### References:
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