Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Generalization of Some Arithmetical Properties of Fermat-Euler Dynamical
  Systems   We study and generalize some arithmetical properties of the classes (2^k+)
and (2^k-) introduced by V. I. Arnold: a number n belongs to the class (N+) if
N|\varphi(n) and 2^{\frac{\varphi(n)}{N}} \equiv 1 mod n where \varphi(n) is
the Euler function, and belongs to the class (M-) if M|\varphi(n) and
2^{\frac{\varphi(n)}{M}} \equiv -1 mod n. The classes (2+), (2-),(4+), (4-),
(8+)and (8-) are studied by V. I. Arnold and here we will show general
properties of the classes (2^k+) and (2^k-) and we will see that the properties
which is proved by V. I. Arnold are special cases of ours.

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The categories of this paper are: quant-ph
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The categories of this paper are: nucl-th
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The categories of this paper are: dg-ga
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The categories of this paper are: cmp-lg
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The categories of this paper are: q-alg
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The categories of this paper are: mtrl-th
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The categories of this paper are: eess
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The categories of this paper are: plasm-ph
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The categories of this paper are: ao-sci
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The categories of this paper are: chem-ph
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The categories of this paper are: supr-con
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The categories of this paper are: alg-geom
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The categories of this paper are: econ
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The categories of this paper are: acc-phys
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The categories of this paper are: adap-org
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The categories of this paper are: hep-th