Abstract
Up to now we have presented several useful applications of the Fermat numbers in number theory, e.g., in proving that there exist infinitely many primes and pseudoprimes, and in establishing the existence of Sierpiński numbers (see Remark 4.2, Theorems 12.1 and 7.4). However, there are more practical applications of F m, as we shall see in this chapter. In particular, we introduce the use of Fermat numbers in number-theoretic transforms; in binary arithmetic modulo F m, which leads to fast multiplication of large numbers; in pseudorandom number generators; in hashing schemes; in the chiral Potts model; and in an analysis of the logistic equation by means of divisors of Fermat numbers.
The advantage of mathematics as a science is that you can check whether you are right or wrong.
Norman Macrae: John von Neumann, 1999, p.139.
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© 2002 Springer Science+Business Media New York
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Křížek, M., Luca, F., Somer, L. (2002). Fermat Number Transform and Other Applications. 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_15
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DOI: https://doi.org/10.1007/978-0-387-21850-2_15
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4419-2952-5
Online ISBN: 978-0-387-21850-2
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