Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Tiling Rectangles and the Plane using Squares of Integral Sides   We study the problem of perfect tiling in the plane and exploring the
possibility of tiling a rectangle using integral distinct squares. Assume a set
of distinguishable squares (or equivalently a set of distinct natural numbers)
is given, and one has to decide whether it can tile the plane or a rectangle or
not. Previously, it has been proved that tiling the plane is not feasible using
a set of odd numbers or an infinite sequence of natural numbers including
exactly two odd numbers. The problem is open for different situations in which
the number of odd numbers is arbitrary. In addition to providing a solution to
this special case, we discuss some open problems to tile the plane and
rectangles in this paper.

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The categories of this paper are: chem-ph
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The categories of this paper are: adap-org
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The categories of this paper are: q-bio
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The categories of this paper are: acc-phys
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The categories of this paper are: funct-an
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The categories of this paper are: ao-sci
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The categories of this paper are: patt-sol
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The categories of this paper are: math-ph
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The categories of this paper are: astro-ph
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The categories of this paper are: chao-dyn
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The categories of this paper are: physics
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The categories of this paper are: atom-ph
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The categories of this paper are: mtrl-th
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The categories of this paper are: nucl-th
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The categories of this paper are: supr-con
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The categories of this paper are: plasm-ph