Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Inverse problems associated with perfect cuboids   A perfect cuboid is a rectangular parallelepiped with integer edges, integer
face diagonals, and integer space diagonal. Such cuboids have not yet been
found, but nor has their existence been disproved. Perfect cuboids are
described by a certain system of Diophantine equations possessing an intrinsic
$S_3$ symmetry. Recently these equations were factorized with respect to this
$S_3$ symmetry and the factor equations were transformed into $E$-form. As
appears, the transformed factor equations are explicitly solvable. Based on
this solution, polynomial inverse problems are formulated in the present paper.

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The categories of this paper are: chao-dyn
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The categories of this paper are: q-fin
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The categories of this paper are: funct-an
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The categories of this paper are: cs
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The categories of this paper are: eess
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The categories of this paper are: acc-phys
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The categories of this paper are: hep-ph
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The categories of this paper are: stat
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The categories of this paper are: solv-int
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The categories of this paper are: supr-con
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The categories of this paper are: math-ph
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The categories of this paper are: hep-th
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The categories of this paper are: nucl-ex
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The categories of this paper are: gr-qc
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The categories of this paper are: ao-sci
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The categories of this paper are: q-alg