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arXiv · 1903.07132

Rational sequences on different models of elliptic curves

Gamze Savaş ÇELİK·Mohammad Sadek·Gökhan Soydan
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Abstract

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 $|S|$ 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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Gamze Savaş ÇELİK, Mohammad Sadek, Gökhan Soydan. 2019-03-17. Rational sequences on different models of elliptic curves. https://arxiv.org/abs/1903.07132

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