Titlebook: Applications of Fibonacci Numbers; Volume 2 A. N. Philippou,A. F. Horadam,G. E. Bergum Book 1988 Springer Science+Business Media B.V. 1988

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Fibonacci Numbers and Groups,of it which are relevant to the present paper. In the remaining sections we discuss links, occurring in our work over a number of years, between this topic and the Fibonacci and Lucas sequences of numbers (f.) and (g.)

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Primes Having an Incomplete System of Residues for a Class of Second-Order Recurrences,established this result for the cases in which p = 1, 9, 11, or 19 modulo 20, while Bruckner proved the result true for the re ma ini n g c ases in which p = 3 or 7 modulo 10. Burr [2] extended these results by dete rmining all the positive integers m for which the Fibonacci sequence has an incomplete system of residues modulo m.

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The Generalized Fibonacci Numbers {Cn}, Cn = Cn-1 + Cn-2 + K,Frank Harary asked one of the authors if they had ever encountered C. = C. + C. + 1, which was used by Harary in connection with something he was counting involving Boolean Algebras. In fact, in Harary’s research it was noticed that the value of one could be replaced by any integer k.

Ingredient

On the Representation of Integral Sequences {Fn/d} and {Ln/d} as Sums of Fibonacci Numbers and as Sal elements in these sequences. Restrictions on n such that F. = 0 (mod d) can always be determined. However, for n ε{5, 8, 10, 12, 13, 15, 16, 17, 20} there does not exist an n-value such that L. = 0 (mod d).

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nd Their Applications. These papers have been selected after a careful review by well known referee‘s in the field, and they range from elementary number theory to probability and statistics. The Fibonacci numbers are their unifying bond. It is anticipated that this book will be useful to research w

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Architecture of Commercial News Systemsurrence relation or an (m+1)th order difference equation. Thus {T.} is an integer sequence. The purpose of our present paper is to generalize results which we obtained [2] for a sequence {T.} defined by a second order recurrence relation (m = 1 in (1)), the Fibonacci and Lucas sequences being important special cases. (The case m = 0 is trivial.)

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Biometrics for User Authenticationest success run in n Bernoulli trials, deriving the probability function of Ln, its distribution function, and its factorial moments. In particular, they found that .and .where .are the Fibnacci-type polynomials of order k [11, 15].

CESS

A Congruence Relation for a Linear Recursive Sequence of Arbitrary Order,urrence relation or an (m+1)th order difference equation. Thus {T.} is an integer sequence. The purpose of our present paper is to generalize results which we obtained [2] for a sequence {T.} defined by a second order recurrence relation (m = 1 in (1)), the Fibonacci and Lucas sequences being important special cases. (The case m = 0 is trivial.)

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