CUBIC FORMULA AND CUBIC CURVES

Title & Authors
CUBIC FORMULA AND CUBIC CURVES
Woo, Sung Sik;

Abstract
The problem of finding rational or integral points of an elliptic 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 polynomial 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 $\small{y^2=x^3+b}$.
Keywords
cubic equation;rational solution;integral point of an elliptic curve;
Language
English
Cited by
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