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Block-Bordered Magic Squares of Prime and Double Prime Orders - III

Inder J. Taneja


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        <foaf:name>Inder J. Taneja</foaf:name>
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            <foaf:name>Formarly, Professor of Mathematics, Federal University of Santa Catarina, Florianópolis, SC, Brazil</foaf:name>
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    <dct:title>Block-Bordered Magic Squares of Prime and Double Prime Orders - III</dct:title>
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    <dct:issued rdf:datatype="http://www.w3.org/2001/XMLSchema#gYear">2020</dct:issued>
    <dcat:keyword>Bordered Magic Squares, Block-Wise Magic Squares</dcat:keyword>
    <dct:issued rdf:datatype="http://www.w3.org/2001/XMLSchema#date">2020-09-01</dct:issued>
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    <dct:description>&lt;p&gt;We know that we can always write &lt;strong&gt;block-wise magic squares&lt;/strong&gt;&amp;nbsp;of any order except for the orders of type &lt;em&gt;p&lt;/em&gt;&amp;nbsp;and &lt;em&gt;2p&lt;/em&gt;, where &lt;em&gt;p&lt;/em&gt;&amp;nbsp;is a prime number. On the other hand we can always write &lt;strong&gt;bordered magic squares&lt;/strong&gt;&amp;nbsp;of any order. The aims of this work is to combine the both, i.e., &lt;strong&gt;bordered&lt;/strong&gt;&amp;nbsp;and &lt;strong&gt;block-wise&lt;/strong&gt;&amp;nbsp;magic squares, for the magic squares of &lt;strong&gt;prime&lt;/strong&gt;&amp;nbsp;and &lt;strong&gt;double prime&lt;/strong&gt;&amp;nbsp;orders. We call it as &lt;strong&gt;block-bordered&lt;/strong&gt;&amp;nbsp;magic squares. The magic squares considered in this work are of orders orders 41, 43, 46, 47 and 51. In order to bring these &lt;strong&gt;block-bordered&lt;/strong&gt;&amp;nbsp;magic squares, we make use of author&amp;#39;s previous works (&lt;a href="http://doi.org/10.5281/zenodo.2555343"&gt;work1&lt;/a&gt;, &lt;a href="http://doi.org/10.5281/zenodo.2555889"&gt;work2&lt;/a&gt;) on block-wise&amp;nbsp;constructions of magics squares, such as, of orders, 39, &amp;nbsp;40, 42, 44, 45, 49 and 51. This is the third part of the work. The first and second parts (&lt;a href="http://doi.org/10.5281/zenodo.3990291"&gt;part1&lt;/a&gt;, &lt;a href="http://doi.org/10.5281/zenodo.3990293"&gt;part2&lt;/a&gt;) works with orders, 10, 11, 13, 14, 17, 19, 22, 26, 29, 31, 34, 37 and 38. The forth part of the work shall be on magic squares of orders 58,&amp;nbsp;59 and 61.&lt;/p&gt;</dct:description>
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