The Order of Appearance of the Product of Five Consecutive Lucas Numbers
and | Mar 11, 2015
Tatra Mountains Mathematical Publications
Special Issue Title: Number Theory ‘14
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.
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
for all positive integers n ≡ 0,8 (mod 12).