Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A remark on Zoloterav's theorem   Let n>=3 be an odd integer. For any integer a prime to n, define the
permutation gamma_{a,n} of {1,...,(n-1)/2} by gamma_{a,n}(x)=n-\dec{ax}_n if
{ax}_n>=(n+1)/2, and {ax}_n if {ax}_n<=(n-1)/2, where {x}_n denotes the least
nonnegative residue of x modulo n. In this note, we show that the sign of
gamma_{a,n} coincides with the Jacobi symbol (a/n) if n=1 mod 4, and 1 if n=3
mod 4.

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The categories of this paper are: hep-ph
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The categories of this paper are: physics
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The categories of this paper are: math-ph
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The categories of this paper are: stat
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The categories of this paper are: nlin
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The categories of this paper are: solv-int
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The categories of this paper are: chem-ph
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The categories of this paper are: chao-dyn
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The categories of this paper are: alg-geom
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The categories of this paper are: funct-an
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The categories of this paper are: cond-mat
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The categories of this paper are: q-bio
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The categories of this paper are: quant-ph
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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: patt-sol