Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Divisibility properties of the Fibonacci entry point   For a prime $p$, let $Z(p)$ be the smallest positive integer $n$ so that $p$
divides $F_{n}$, the $n$th term in the Fibonacci sequence. Paul Bruckman and
Peter Anderson conjectured a formula for $\zeta(m)$, the density of primes $p$
for which $m | Z(p)$ on the basis of numerical evidence. We prove Bruckman and
Anderson's conjecture by studying the algebraic group $G : x^{2} - 5y^{2} = 1$
and relating $Z(p)$ to the order of $\alpha = (3/2,1/2) \in G(\F_{p})$. We are
then able to use Galois theory and the Chebotarev density theorem to compute
$\zeta(m)$.

35
The categories of this paper are: mtrl-th
26
The categories of this paper are: bayes-an
29
The categories of this paper are: funct-an
5
The categories of this paper are: gr-qc
7
The categories of this paper are: hep-th
13
The categories of this paper are: quant-ph
25
The categories of this paper are: patt-sol
15
The categories of this paper are: nucl-ex
30
The categories of this paper are: q-alg
14
The categories of this paper are: math-ph
22
The categories of this paper are: chao-dyn
37
The categories of this paper are: supr-con
9
The categories of this paper are: nlin
16
The categories of this paper are: stat
1
The categories of this paper are: cs
28
The categories of this paper are: alg-geom