Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Sums of four rational squares with certain restrictions   In this paper we mainly study sums of four rational squares with certain
restrictions. Let $\mathbb Q_{\ge0}$ be the set of nonnegative rational
numbers. We establish the following four-square theorem for rational numbers:
For any $a,b,c,d\in\mathbb Q_{\ge0}$, each $r\in\mathbb Q_{\ge0}$ can be
written as $x^2+y^2+z^2+w^2$ with $x,y,z,w\in\mathbb Q_{\ge0}$ such that
$ax+by+cz+dw$ is a rational square (or a rational cube). This paper also
contains many conjectures; for example, for any positive integers $a$ and $b$
with $\gcd(a,b)=1$, we conjecture that each $r\in\mathbb Q_{\ge0}$ can be
written as $aw^4+bx^4+y^2+z^2$ with $w,x,y,z\in\mathbb Q$.

14
The categories of this paper are: math-ph
12
The categories of this paper are: nucl-th
28
The categories of this paper are: alg-geom
20
The categories of this paper are: acc-phys
11
The categories of this paper are: hep-lat
22
The categories of this paper are: chao-dyn
34
The categories of this paper are: chem-ph
36
The categories of this paper are: cmp-lg
32
The categories of this paper are: atom-ph
25
The categories of this paper are: patt-sol
26
The categories of this paper are: bayes-an
9
The categories of this paper are: nlin
1
The categories of this paper are: cs
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The categories of this paper are: nucl-ex
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The categories of this paper are: eess
27
The categories of this paper are: comp-gas