On New Formulas of Fibonacci and Lucas Numbers Involving Golden Ratio Associated with Atomic Structure in Chemistry

Some New Finite Sums Involving Generalized Fibonacci And Lucas Numbers

Equations Involving Arithmetic Functions of Fibonacci and Lucas Numbers

For any positive integer k, let (k) and a(k) be the number of positive integers less than or equal to k and relatively prime to k and the sum of divisors ofk, respectively. In [6] we have shown that 0(Fn) > F^n) and that a(Fn) < Fa{ri) and we have also determined all the cases in which the above inequalities become equalities. A more general inequality of this type was proved in [7]. In [8] ...

Some Trigonometric Identities Involving Fibonacci and Lucas Numbers

In this paper, using the number of spanning trees in some classes of graphs, we prove the identities: Fn = 2n−1 n √

Identities Involving Lucas or Fibonacci and Lucas Numbers as Binomial Sums

As in [1, 2], for rapid numerical calculations of identities pertaining to Lucas or both Fibonacci and Lucas numbers we present each identity as a binomial sum. 1. Preliminaries The two most well-known linear homogeneous recurrence relations of order two with constant coefficients are those that define Fibonacci and Lucas numbers (or Fibonacci and Lucas sequences). They are defined recursively ...

A New Cryptography Model via Fibonacci and Lucas Numbers

Coding/decoding algorithms are of great importance to help in improving information security since information security is a more significiant problem in recent years. In this paper we introduce two new coding/decoding algorithms using Fibonacci $Q$-matrices and $R$-matrices. Our models are based on the blocked message matrices and the encryption of each message matrix with different keys. Thes...