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http://dx.doi.org/10.4134/CKMS.2013.28.4.723

BACHET EQUATIONS AND CUBIC RESOLVENTS

Woo, Sung Sik (Department of Mathematics College of Natural Science Ewha Womans University)

Publication Information

Communications of the Korean Mathematical Society / v.28, no.4, 2013 , pp. 723-733 More about this Journal

Abstract

A Bachet equation $Y^2=X^3+k$ will have a rational solution if and only if there is $b{\in}\mathbb{Q}$ for which $X^3-b^2X^2+k$ 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;

Citations & Related Records

Reference

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