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A problematic identity

Published online by Cambridge University Press:  26 February 2010

H. Davenport
H. Davenport
Affiliation:
Trinity College, Cambridge.
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Extract

The following problem was proposed by Professor N. J. Fine: to prove that there do not exist rational functions F1, F2, F3 of x1, x2, x3, x4, with real coefficients, such that

identically. In the present note I give a proof.†

Type
Research Article
Information
Mathematika , Volume 10 , Issue 1 , June 1963 , pp. 10 - 12
Copyright
Copyright © University College London 1963

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References

† Dr. Cassels, to whom I communicated this note, has obtained a more general result, which will be published shortly in Acta Arithmetica.

† See Perron, Algebra I, Satz 117 and Satz 118.