Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the periodicity of an algorithm for p-adic continued fractions   In this paper we study the properties of an algorithm for generating
continued fractions in the field of p-adic numbers $\mathbb{Q}_p$. First of
all, we obtain an analogue of the Galois' Theorem for classical continued
fractions. Then, we investigate the length of the preperiod for periodic
expansions of square roots. Finally, we prove that there exist infinitely many
square roots of integers in $\mathbb{Q}_p$ that have a periodic expansion with
period of length four, solving an open problem left by Browkin.

8
The categories of this paper are: hep-ex
12
The categories of this paper are: nucl-th
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The categories of this paper are: comp-gas
13
The categories of this paper are: quant-ph
15
The categories of this paper are: nucl-ex
14
The categories of this paper are: math-ph
18
The categories of this paper are: econ
34
The categories of this paper are: chem-ph
26
The categories of this paper are: bayes-an
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The categories of this paper are: q-alg
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The categories of this paper are: gr-qc
22
The categories of this paper are: chao-dyn
33
The categories of this paper are: plasm-ph
29
The categories of this paper are: funct-an
3
The categories of this paper are: physics
32
The categories of this paper are: atom-ph