Geodesic
Rational Bézier curves with infinitely many integral points
Archivum mathematicum, Tome 59 (2023) no. 4, pp. 339-349 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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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.
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.
DOI : 10.5817/AM2023-4-339
Classification : 14H25, 14H45, 14H50, 14Q05, 65D17
Keywords: Bézier curve; rational Bézier curve; curve of genus 0; integral point 
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     title = {Rational {B\'ezier} curves with infinitely many integral points},
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     url = {http://geodesic.mathdoc.fr/articles/10.5817/AM2023-4-339/}
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Dospra, Petroula. Rational Bézier curves with infinitely many integral points. Archivum mathematicum, Tome 59 (2023) no. 4, pp. 339-349. doi: 10.5817/AM2023-4-339

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