Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A reinforcement of the Bourgain-Kontorovich's theorem by elementary
  methods II   Zaremba's conjecture (1971) states that every positive integer number $d$ can
be represented as a denominator (continuant) of a finite continued fraction
$\frac{b}{d}=[d_1,d_2,...,d_{k}],$ with all partial quotients
$d_1,d_2,...,d_{k}$ being bounded by an absolute constant $A.$ Recently (in
2011) several new theorems concerning this conjecture were proved by Bourgain
and Kontorovich. The easiest of them states that the set of numbers satisfying
Zaremba's conjecture with A=50 has positive proportion in $\N.$ In this
paper,using only elementary methods, the same theorem is proved with A=5.

14
The categories of this paper are: math-ph
24
The categories of this paper are: dg-ga
10
The categories of this paper are: q-bio
21
The categories of this paper are: adap-org
3
The categories of this paper are: physics
28
The categories of this paper are: alg-geom
5
The categories of this paper are: gr-qc
7
The categories of this paper are: hep-th
22
The categories of this paper are: chao-dyn
26
The categories of this paper are: bayes-an
4
The categories of this paper are: cond-mat
12
The categories of this paper are: nucl-th
8
The categories of this paper are: hep-ex
37
The categories of this paper are: supr-con
36
The categories of this paper are: cmp-lg
18
The categories of this paper are: econ