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The Theory of Circulants in the Historical Order of Development up to 1860

Published online by Cambridge University Press:  15 September 2014

Thomas Muir
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Extract

So far as mathematical writers have as yet noted, a set of equations of the type

had not made its appearance in mathematical work prior to the year 1846: and it is almost absolutely certain that before that year the determinant of such a set had never been considered. It is not at all unlikely, however, that the expression

which is the case of the determinant for n equal to 3 had more than once turned up in other connections, and that its divisibility by a + b + c had been noted: but of this, too, there is no record.

Type
Proceedings
Information
Proceedings of the Royal Society of Edinburgh , Volume 26 , Issue 1 , 1906 , pp. 390 - 398
Copyright
Copyright © Royal Society of Edinburgh 1906

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References

page 392 note * This result is reached in a way different from Catalan's by performing on Δ' the operation

separating out the factor n, and then showing that the resulting determinant is ( − 1)n−1Δ.