Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On binary quadratic forms with semigroup property   A quadratic form f is said to have semigroup property if its values at points
of the integer lattice form a semigroup under multiplication. A problem of V.
Arnold is to describe all binary integer quadratic forms with semigroup
property. If there is an integer bilinear map s such that f(s(x,y))=f(x)f(y)
for all vectors x and y from the integer 2-dimensional lattice, then the form f
has semigroup property. We give an explicit description of all pairs (f,s) with
the property stated above. We do not know any other examples of forms with
semigroup property.

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The categories of this paper are: q-fin
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The categories of this paper are: physics
31
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: hep-th
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The categories of this paper are: adap-org
30
The categories of this paper are: q-alg
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The categories of this paper are: nucl-th
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The categories of this paper are: supr-con
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The categories of this paper are: hep-ph
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The categories of this paper are: math-ph
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The categories of this paper are: quant-ph
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The categories of this paper are: hep-lat
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The categories of this paper are: cmp-lg
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The categories of this paper are: eess
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The categories of this paper are: atom-ph