Communications of the Korean Mathematical Society (대한수학회논문집)

Korean Mathematical Society (대한수학회)
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BACHET EQUATIONS AND CUBIC RESOLVENTS

  • Woo, Sung Sik (Department of Mathematics College of Natural Science Ewha Womans University)
  • Received : 2012.12.17
  • Published : 2013.10.31
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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.

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References

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