GEOMETRIC PROGRESSIONS ON ELLIPTIC CURVES ABDOUL AzIz CIss AND DUsTIN MOODY Ecole Polytechnique de Thies, Senegal National Institute of Standards and Technology, United States of America
نویسنده
چکیده
In this paper, we look at long geometric progressions on diferent model of elliptic curves, namely Weierstrass curves, Edwards and twisted Edwards curves, Huf curves and general quartics curves. By a geometric progression on an elliptic curve, we mean the existence of rational points on the curve whose x-coordinate (or y-coordinate) are in geometric progression. We fnd infnite families of twisted Edwards curves and Huf curves with geometric progressions of length 5, an infnite family of Weierstrass curves with 8 term progressions, as well as infnite families of quartic curves containing 10-term geometric progressions.
منابع مشابه
Geometric Progressions on Elliptic Curves.
In this paper, we look at long geometric progressions on different model of elliptic curves, namely Weierstrass curves, Edwards and twisted Edwards curves, Huff curves and general quartics curves. By a geometric progression on an elliptic curve, we mean the existence of rational points on the curve whose x-coordinate (or y-coordinate) are in geometric progression. We find infinite families of t...
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