Abstract
What really made everything tick in Chapter 11 was Lemma 11.4:
. Unfortunately, few continued fraction expansions satisfy such a nice relationship. It was Lucas’ idea to concentrate on those sequences that do whether or not they arise from a continued fraction expansion.
“The Mathematicians are a sort of Frenchmen: when you talk to them, they immediately translate it into their own language, and right away it is something utterly different.”
- Johann Wolfgang Von Goethe
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References
John Brillhart, D. H. Lehmer and J. L. Selfridge, “New primality criteria and factorizations of 2m ± 1,” Math. of Computation, 29(1975), 620–647.
D. H. Lehmer, “An extended theory of Lucas functions,” Annals of Math. 31(1930), 419–448.
Edouard Lucas, “Théorie des fonctions numériques simplement périodiques,” Amer. J. of Math., 1(1878), 184–240, 289-321.
Hugh Williams, “A p + 1 method of factoring,” Math. of Computation, 39(1982), 225–234.
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© 1989 Springer-Verlag New York, Inc.
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Bressoud, D.M. (1989). Lucas Sequences. In: Factorization and Primality Testing. Undergraduate Texts in Mathematics. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-4544-5_12
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DOI: https://doi.org/10.1007/978-1-4612-4544-5_12
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