Let $ F_n$ be the $n$th Fibonacci number and let $L_n$ be the $n$th 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 $F_k$. For instance, $z(F_n)=n=z(L_n)/2$, for all $n>2$. In this paper, among other things, we prove that\begin{center} $z(L_{n}L_{n+1}L_{n+2}L_{n+3}L_{n+4})=\dfrac{n(n+1)(n+2)(n+3)(n+4)}{12}$,\end{center}for all positive integers $n\equiv 0,8\pmod{12}$.
@article{324,
title = {The order of appearance of the product of five consecutive Lucas numbers},
journal = {Tatra Mountains Mathematical Publications},
volume = {58},
year = {2014},
doi = {10.2478/tatra.v59i0.324},
language = {EN},
url = {http://dml.mathdoc.fr/item/324}
}
Marques, Diego; Trojovský, Pavel. The order of appearance of the product of five consecutive Lucas numbers. Tatra Mountains Mathematical Publications, Tome 58 (2014) . doi : 10.2478/tatra.v59i0.324. http://gdmltest.u-ga.fr/item/324/