Integer and Rational Solutions to Polynomial Equations
Abstract
A formalism is given to count integer and rational solutions to polynomial equations with rational coefficients. These polynomials P(x) are parameterized by three integers, labeling an elliptic curve. The counting of the rational solutions to y2=P(x) is facilitated by another elliptic curve with integral coefficients. The problem of counting is described by two elliptic curves and a map between them.
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