Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The general case on the order of appearance of product of consecutive
  Fibonacci and Lucas numbers   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 Fibonacci
sequence, 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 to
the case $z(F_{n}F_{n+1}\cdots F_{n+k})$ for every $4\leq k \leq 6$. We also
give a formula for $z(L_nL_{n+1}\cdots L_{n+k})$ when $k = 5,6$ which extends
the recent result of Marques and Trojovsk\'y. Our method gives a general idea
on 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 $k\geq 1$.

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The categories of this paper are: chem-ph
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The categories of this paper are: q-fin
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The categories of this paper are: ao-sci
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The categories of this paper are: mtrl-th
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The categories of this paper are: adap-org
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The categories of this paper are: solv-int
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The categories of this paper are: cond-mat
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The categories of this paper are: nucl-ex
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The categories of this paper are: q-bio
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The categories of this paper are: atom-ph
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The categories of this paper are: quant-ph
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The categories of this paper are: stat
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The categories of this paper are: econ
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The categories of this paper are: math-ph
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The categories of this paper are: alg-geom
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The categories of this paper are: hep-ex