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On a quartic diophantine equation

Published online by Cambridge University Press:  20 January 2009

R. J. Stroeker  and
B. M. M. De Weger
R. J. Stroeker
Affiliation:
Econometric Institute Erasmus University P.O. Box 1738 3000 Dr Rotterdam The Netherlands E-mail address: [email protected], [email protected]
B. M. M. De Weger
Affiliation:
Econometric Institute Erasmus University P.O. Box 1738 3000 Dr Rotterdam The Netherlands E-mail address: [email protected], [email protected]
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Abstract

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In this paper we consider the quartic diophantine equation 3(y2 – 1) = 2x2(x2 – 1) in integers x and y. We show that this equation does not have any other solutions (x, y) with x≧0 than those given by x = 0,1,2,3,6,91. Two approaches are emphasized, one based on diophantine approximation techniques, the other depends on the structure of certain quartic number fields.

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 39 , Issue 1 , February 1996 , pp. 97 - 114
Copyright
Copyright © Edinburgh Mathematical Society 1996

References

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