Abstract
The factors k2n +1, k, n ∈ ℕ of Fermat numbers have been intensively studied by many authors, e.g., [Artjuhov], [Banlie], [Bosma], [Brent, 1982], [Brillhart, Lehmer, Selfridge], [Cormack, Williams], [Golomb, 1976], [Keller 1983, 1992], [Křížek, Chleboun, 1994, 1997], [Papademetrios], [Shorey, Stewart], [Williams, 1988]. In 1878, F. Proth stated the following theorem (see [Proth, 1878b, 1978c] and see [Robinson, 1957b], [Sierpiński, 1964a] for proofs of this theorem), which can be applied to verify easily the primality of divisors of Fermat numbers for k < 2n (see [Robinson, 1957a] and [Robinson, 1958]; also compare with Suyama’s Theorem 4.22).
Numbers constitute the only universal language.
Nathanael West
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© 2002 Springer Science+Business Media New York
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Křížek, M., Luca, F., Somer, L. (2002). Factors of Fermat Numbers. In: 17 Lectures on Fermat Numbers. CMS Books in Mathematics / Ouvrages de mathématiques de la SMC. Springer, New York, NY. https://doi.org/10.1007/978-0-387-21850-2_7
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DOI: https://doi.org/10.1007/978-0-387-21850-2_7
Publisher Name: Springer, New York, NY
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