English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

Let $F_{n}$ and $L_n$ be the $n$th Fibonacci and Lucas number, respectively.For each positive integer $m$, the order of appearance of $m$ in the Fibonaccisequence, denoted by $z(m)$, is the smallest positive integer $k$ such that $m$divides $F_k$. Recently, D. Marques has obtained a formula for$z(F_{n}F_{n+1})$, $z(F_{n}F_{n+1}F_{n+2})$, and$z(F_{n}F_{n+1}F_{n+2}F_{n+3})$. In this paper, we extend Marques' result tothe case $z(F_{n}F_{n+1}\cdots F_{n+k})$ for every $4\leq k \leq 6$. We alsogive a formula for $z(L_nL_{n+1}\cdots L_{n+k})$ when $k = 5,6$ which extendsthe recent result of Marques and Trojovsk\'y. Our method gives a general ideaon how to obtain the formulas for $z(F_nF_{n+1}\cdots F_{n+k})$ and$z(L_nL_{n+1}\cdots L_{n+k})$ for every $k\geq 1$.

The general case on the order of appearance of product of consecutive Fibonacci and Lucas numbers