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The diophantine equation Ax4 + By4 + Cz4 = 0

Published online by Cambridge University Press:  24 October 2008

L. J. Mordell
L. J. Mordell
Affiliation:
St John's College, Cambridge
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Extract

In a paper (1) published in 1922 in these Proceedings, I conjectured that a curve of genus greater than one contained only a finite number of rational points, but this has never been proved. A particular case is given by the equation of genus three,

and so any results for such equations may be of interest.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 68 , Issue 1 , July 1970 , pp. 125 - 128
Copyright
Copyright © Cambridge Philosophical Society 1970

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References

REFERENCES

(1)Mordell, L. J.On the rational solutions of the indeterminate equations of the third and fourth degrees. Proc. Cambridge Philos. Soc. 21 (1922), 179–192.Google Scholar
(2)Mordell, L. J.Some quartic diophantine equations of genus 3. Proc. Amer. Math. Soc. 17 (1966), 1152–1158.CrossRefGoogle Scholar