Rational sequences on different models of elliptic curves
Çelik, Gamze Savaş and Sadek, Mohammad and Soydan, Gökhan (2019) Rational sequences on different models of elliptic curves. Glasnik Matematicki, 54 (1). pp. 53-64. ISSN 0017-095X (Print) 1846-7989 (Online)
Official URL: http://dx.doi.org/10.3336/gm.54.1.04
Given a set S of elements in a number field k, we discuss the existence of planar algebraic curves over k which possess rational points whose x-coordinates are exactly the elements of S. If the size vertical bar S vertical bar of S is either 4, 5, or 6, we exhibit infinite families of (twisted) Edwards curves and (general) Huff curves for which the elements of S are realized as the x-coordinates of rational points on these curves. This generalizes earlier work on progressions of certain types on some algebraic curves.
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