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Cubic formula and cubic curves

Title
Cubic formula and cubic curves
Authors
Woo S.S.
Ewha Authors
우성식
SCOPUS Author ID
우성식scopus
Issue Date
2013
Journal Title
Communications of the Korean Mathematical Society
ISSN
1225-1763JCR Link
Citation
vol. 28, no. 2, pp. 209 - 224
Indexed
SCOPUS; KCI scopus
Abstract
The problem of finding rational or integral points of an ellip-tic curve basically boils down to solving a cubic equation. We look closely at the cubic formula of Cardano to find a criterion for a cubic polyno-mial to have a rational or integral roots. Also we show that existence of a rational root of a cubic polynomial implies existence of a solution for certain Diophantine equation. As an application we find some integral solutions of some special type for y2 = x3 + b. © 2013 The Korean Mathematical Society.
DOI
10.4134/CKMS.2013.28.2.209
Appears in Collections:
자연과학대학 > 수학전공 > Journal papers
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