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The ‘odd’ number six

Published online by Cambridge University Press:  24 October 2008

J. A. Todd
J. A. Todd
Affiliation:
Trinity CollegeCambridge
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Extract

1. A few months ago, in the course of teaching an elementary class. I had occasion to discuss problems of the familiar type, ‘if α, β, γ are the roots of the equation x3 + qx + r = 0, form the equation whose roots are α2 + βγ, β2 + γα, γ2 + αβ'. After I had explained the device of replacing βγ by αβγ/α = −r/α, so that the roots of the new equation are the same rational function of the separate roots of the original equation, I was asked ‘whether such a transformation was always possible’. On investigation the answer to the question proved to be a surprising one.

Type
Research Notes
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 41 , Issue 1 , June 1945 , pp. 66 - 68
Copyright
Copyright © Cambridge Philosophical Society 1945

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References

† Burnside, , Theory of Groups of Finite Order, 2nd ed. (Cambridge, 1911), p. 209.Google Scholar

† Sylvester, , Collected Papers, 1, p. 92Google Scholar. See, e.g., Baker, , Principles of Geometry, 2 (Cambridge, 1922), p. 221Google Scholar, and some remarks by Room, , Geometry of Determinantal Loci (Cambridge, 1938), p. 301.Google Scholar

‡ Baker, loc. cit.