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Published online by Cambridge University Press: 26 February 2010
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.†
† 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.