논문KCI 등재
Bachet equations and cubic resolvents
대한수학회 (The Korean Mathematical Society)|2013.10|대한수학회논문집 (Communications of the KMS)|제28권 제4호|pp. 723-733
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A Bachet equation Y 2 = X3+k will have a rational solutionif and only if there is b ∈ Q for which X3 −b2X2 +k is reducible. In thispaper we show that such cubics arise as a cubic resolvent of a biquadraticpolynomial. And we prove various properties of cubic resolvents.
Abstract
A Bachet equation Y 2 = X3+k will have a rational solutionif and only if there is b ∈ Q for which X3 −b2X2 +k is reducible. In thispaper we show that such cubics arise as a cubic resolvent of a biquadraticpolynomial. And we prove various properties of cubic resolvents.
참고문헌 (4)
- D. A. Cox, "Galois Theory" (2004), Wiley-Interscience
- K. Ireland, "A Classical Introduction to Modern Number Theory" (1990), Springer-Verlag
- A. Schinzel, "Polynomials with Special Regard to Reducibility, In Encyclopedia of mathemat- ics and its applications 77" (2000), Cambridge University Press
- B. L. van der Waerden, "Algebra" (1967), Frederick Ungar Publishing Co.
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