Bachet equations and cubic resolvents
Commun. Korean Math. Soc. 2013 Vol. 28, No. 4, 723-733
https://doi.org/10.4134/CKMS.2013.28.4.723
Printed October 1, 2013
Sung Sik Woo
Ewha Womans University
Abstract : A Bachet equation $Y^2=X^3+k$ will have a rational solution if and only if there is $b\in \Q$ 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
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