<abstract xmlns="http://www.w3.org/1999/xhtml"> Let Fn be the nth Fibonacci number and let Ln be the nth Lucas number. The order of appearance z(n) of a natural number n is defined as the smallest natural number k such that n divides Fk. For instance, z(Fn) = n = z(Ln)/2 for all n > 2. In this paper, among other things, we prove that<inline-formula><alternatives><inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="graphic/Untitled-1.jpg"></inline-graphic></alternatives></inline-formula>for all positive integers n ≡ 0,8 (mod 12).</abstract>

Let Fn be the nth Fibonacci number and let Ln be the nth Lucas number. The order of appearance z(n) of a natural number n is defined as the smallest natural number k such that n divides Fk. For instance, z(Fn) = n = z(Ln)/2 for all n > 2. In this paper, among other things, we prove thatfor all positive integers n ≡ 0,8 (mod 12).

The Order of Appearance of the Product of Five Consecutive Lucas Numbers

Departamento de Matemática Universidade de Brasília 70910-900 Brasília, DF Brazil

Departament of Mathematics Faculty of Science University of Hradec Králové Rokitanského 62 500 03 Hradec Králové Czech Republic

Tatra Mountains Mathematical Publications

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

{"article-title":"The Order of Appearance of the Product of Five Consecutive Lucas Numbers"}

Let Fn be the nth Fibonacci number and let Ln be the nth Lucas number. The order of appearance z(n) of a natural number n is defined as the smallest natural...

The Order of Appearance of the Product of Five Consecutive Lucas Numbers

Published Online: Mar 11, 2015

Page range: 65 - 77

Received: Sep 02, 2014

DOI: https://doi.org/10.2478/tmmp-2014-0019

© 2015

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.