BACHET EQUATIONS AND CUBIC RESOLVENTS

Title & Authors
BACHET EQUATIONS AND CUBIC RESOLVENTS
Woo, Sung Sik;

Abstract
A Bachet equation $\small{Y^2=X^3+k}$ will have a rational solution if and only if there is $\small{b{\in}\mathbb{Q}}$ for which $\small{X^3-b^2X^2+k}$ is reducible. In this paper we show that such cubics arise as a cubic resolvent of a biquadratic polynomial. And we prove various properties of cubic resolvents.
Keywords
Bachet equation;rational solution;resolvent cubi;
Language
English
Cited by
References
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