Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Lattice Equable Quadrilaterals I -- Parallelograms   This paper studies equable parallelograms whose vertices lie on the integer
lattice. Using Rosenberger's Theorem on generalised Markov equations, we show
that the g.c.d. of the side lengths of such parallelograms can only be 3, 4 or
5, and in each of these cases the set of parallelograms naturally forms an
infinite tree all of whose vertices have degree 4, bar the root. The paper then
focuses on what we call Pythagorean equable parallelograms. These are lattice
equable parallelograms whose complement in a circumscribing rectangle consists
of two Pythagorean triangles. We prove that for these parallelograms the
shortest side can only be 3, 4, 5, 6 or 10, and there are five infinite
families of such parallelograms, given by solutions to corresponding Pell-like
equations.

17
The categories of this paper are: q-fin
4
The categories of this paper are: cond-mat
34
The categories of this paper are: chem-ph
37
The categories of this paper are: supr-con
16
The categories of this paper are: stat
25
The categories of this paper are: patt-sol
8
The categories of this paper are: hep-ex
14
The categories of this paper are: math-ph
19
The categories of this paper are: eess
32
The categories of this paper are: atom-ph
15
The categories of this paper are: nucl-ex
1
The categories of this paper are: cs
9
The categories of this paper are: nlin
5
The categories of this paper are: gr-qc
10
The categories of this paper are: q-bio
27
The categories of this paper are: comp-gas