Displaying similar documents to “The real field with the rational points of an elliptic curve”

Rational Bézier curves with infinitely many integral points

Petroula Dospra (2023)

Archivum Mathematicum

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In this paper we consider rational Bézier curves with control points having rational coordinates and rational weights, and we give necessary and sufficient conditions for such a curve to have infinitely many points with integer coefficients. Furthermore, we give algorithms for the construction of these curves and the computation of theirs points with integer coefficients.

Solving an indeterminate third degree equation in rational numbers. Sylvester and Lucas

Tatiana Lavrinenko (2002)

Revue d'histoire des mathématiques

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This article concerns the problem of solving diophantine equations in rational numbers. It traces the way in which the 19th century broke from the centuries-old tradition of the purely algebraic treatment of this problem. Special attention is paid to Sylvester’s work “On Certain Ternary Cubic-Form Equations” (1879–1880), in which the algebraico-geometrical approach was applied to the study of an indeterminate equation of third degree.