Publication: Rational sequences on different models of elliptic curves
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Sadek, Mohammad
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Croatian Mathematical Soc
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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 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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Keywords
Arithmetic progressions, Geometric progressions, Elliptic curve, Edwards curve, Huff curve, Rational sequence, Rational point, Science & technology, Physical sciences, Mathematics, applied, Mathematics