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On the Determinants of Pan-Magic Squares of Even Order

Published online by Cambridge University Press:  03 November 2016

N. Chater  and
W. J. Chater
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Extract

In Mathematical Note 1911, this journal, Vol. XXX, No. 290, A. H. MacColl forms the determinant Δ of a pan-magic square of order 4 and states that Δ = 0. He also remarks that “the property appears to be peculiar to pan-magic squares of order 4”. Below we give our demonstration of the above theorem and extend it to the determinants of all pan-magic squares of even order. We shall show that the determinants of all pan-magic squares of even order have zero as their value. In the proof that follows below we make use of a property of pan-magic squares of even order.

Type
Research Article
Information
The Mathematical Gazette , Volume 33 , Issue 304 , May 1949 , pp. 94 - 98
Copyright
Copyright © Mathematical Association 1949

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