Communications of the
Korean Mathematical Society CKMS

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