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Titlebook: Applications of Fibonacci Numbers; Volume 4 Proceedings G. E. Bergum,A. N. Philippou,A. F. Horadam Conference proceedings 1991 Springer Sci

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Encyclopedia of Molecular PharmacologyLet a triangle in which the vertex angle is a positive integral multiple n of a base angle be called an α — nα triangle. We find integral solutions for the lengths of the sides by a recursive method. We note that, for any particular α for which there is an integral α — nα triangle, cos α must be a rational number by the law of cosines.
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Markus Grube,Gabriele JedlitschkyGeneralizing the Fibonacci search we define the Fibonacci search of degree .. Like the Fibonacci search, which it reduces to for . = 2, the Fibonacci search of degree . involves only addition and subtraction.
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Markus Grube,Gabriele JedlitschkyThe representation of Fibonacci and Lucas numbers in terms of hyperbolic functions [9, p. 7 ff.] and the idea of deriving Fibonacci identities from known hyperbolic identities are not new (e.g., see [6]).
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https://doi.org/10.1007/978-3-030-57401-7Let us consider the Fibonacci polynomials ..(.) and the Lucas polynomials ... (or simply .. and V., if there is no danger of confusion) defined as.and.where . is an indeterminate. These polynomials are a natural extension of the numbers ..(m) and ..(.) considered in [1]. They have already been considered elsewhere (e.g., see [6]).
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https://doi.org/10.1007/978-3-030-57401-7The purpose of this investigation is to exhibit some of the fundamental properties of., the .
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On the Proof of GCD and LCM Equalities Concerning the Generalized Binomial and Multinomial CoefficiA strong divisibility sequence (or SDS) is a sequence of nonzero integers { a. } (n=1, 2, 3,…)that satisfies.for any positive integers m, n, where (a, b) stands for the greatest common divisor of a and b. This terminology was named by Kimberling [7], although this concept had been studied before by Ward [9] and others.
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