Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A note on the multiplicative structure of an additively shifted product
  set, AA+1   We consider the multiplicative structure of sets of the form AA+1, where
where A is a large, finite set of real numbers. In particular, we show that the
additively shifted product set, AA+1 must have a large part outside of any
generalized geometric progression of comparable length. We prove an analogous
result in finite fields as well.

13
The categories of this paper are: quant-ph
33
The categories of this paper are: plasm-ph
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The categories of this paper are: patt-sol
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The categories of this paper are: acc-phys
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The categories of this paper are: alg-geom
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The categories of this paper are: stat
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The categories of this paper are: dg-ga
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The categories of this paper are: hep-lat
36
The categories of this paper are: cmp-lg
26
The categories of this paper are: bayes-an
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The categories of this paper are: cs
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The categories of this paper are: atom-ph
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The categories of this paper are: ao-sci
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The categories of this paper are: math-ph
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The categories of this paper are: adap-org
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The categories of this paper are: supr-con