Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Magic squares with empty cells   A k-magic square of order n is an arrangement of the numbers from 0 to kn-1
in an n by n matrix, such that each row and each column has exactly k filled
cells, each number occurs exactly once, and the sum of the entries of any row
or any column is the same. A magic square is called k-diagonal if its entries
all belong to k consecutive diagonals. In this paper we prove that a k-diagonal
magic square exists if and only if n = k = 1 or 3 <= k <=n and n is odd or k is
even.

9
The categories of this paper are: nlin
1
The categories of this paper are: cs
35
The categories of this paper are: mtrl-th
37
The categories of this paper are: supr-con
32
The categories of this paper are: atom-ph
18
The categories of this paper are: econ
31
The categories of this paper are: ao-sci
36
The categories of this paper are: cmp-lg
33
The categories of this paper are: plasm-ph
12
The categories of this paper are: nucl-th
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The categories of this paper are: acc-phys
19
The categories of this paper are: eess
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The categories of this paper are: astro-ph
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The categories of this paper are: gr-qc
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The categories of this paper are: patt-sol
21
The categories of this paper are: adap-org