A new approach to Fibonacci Tessarines with Fibonacci and Lucas number components

New Fibonacci and Lucas primes

Extending previous searches for prime Fibonacci and Lucas numbers, all probable prime Fibonacci numbers Fn have been determined for 6000 < n ≤ 50000 and all probable prime Lucas numbers Ln have been determined for 1000 < n ≤ 50000. A rigorous proof of primality is given for F9311 and for numbers Ln with n = 1097, 1361, 4787, 4793, 5851, 7741, 10691, 14449, the prime L14449 having 3020 digits. P...

Fibonacci-Lucas densities

Both Fibonacci and Lucas numbers can be described combinatorially in terms of 0− 1 strings without consecutive ones. In the present article we explore the occupation numbers as well as the correlations between various positions in the corresponding configurations. (2000) Mathematics Subject Classification: 11B39, 05A15

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...

Some New Finite Sums Involving Generalized Fibonacci And Lucas Numbers

Maximal hypercubes in Fibonacci and Lucas cubes

The Fibonacci cube Γn is the subgraph of the hypercube induced by the binary strings that contain no two consecutive 1’s. The Lucas cube Λn is obtained 5 from Γn by removing vertices that start and end with 1. We characterize maximal induced hypercubes in Γn and Λn and deduce for any p ≤ n the number of maximal p-dimensional hypercubes in these graphs.