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Generalized Fibonacci Pseudoprimes and Probable Primes

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Applications of Fibonacci Numbers

Abstract

Several mathematical procedures require the provision of large “random” prime numbers. Fermat’s Little Theorem plays an important role in many primality tests and in motivating the concept of pseudoprimes. It tells us that for a prime number n and an integer b with gcd(b, n) = 1 the congruence b n −1 ≡ 1 mod n holds. An alternative formulation of Fermat’s Little Theorem states that for any prime n and an arbitrary integer b one has

$$ {b^n} \equiv b\;\bmod \,n. $$
(1)

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© 1993 Springer Science+Business Media Dordrecht

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Müller, W.B., Oswald, A. (1993). Generalized Fibonacci Pseudoprimes and Probable Primes. In: Bergum, G.E., Philippou, A.N., Horadam, A.F. (eds) Applications of Fibonacci Numbers. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-2058-6_45

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  • DOI: https://doi.org/10.1007/978-94-011-2058-6_45

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-94-010-4912-2

  • Online ISBN: 978-94-011-2058-6

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