Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the integers of the form $p^2+b^2+2^n$ and $b_1^2+b_2^2+2^{n^2}$   We prove that the sumset {p^2+b^2+2^n: p is prime and b,n\in N} has positive
lower density. We also construct a residue class with odd modulo, which
contains no integer of the form p^2+b^2+2^n. And similar results are
established for the sumset {b_1^2+b_2^2+2^{n^2}: b_1,b_2,n\in N}.

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The categories of this paper are: bayes-an
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The categories of this paper are: nucl-th
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The categories of this paper are: atom-ph
0
The categories of this paper are: hep-ph
3
The categories of this paper are: physics
36
The categories of this paper are: cmp-lg
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The categories of this paper are: acc-phys
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The categories of this paper are: stat
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The categories of this paper are: ao-sci
1
The categories of this paper are: cs
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The categories of this paper are: q-alg
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The categories of this paper are: eess
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The categories of this paper are: alg-geom
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The categories of this paper are: astro-ph
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The categories of this paper are: q-fin
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The categories of this paper are: nlin