Sadek, Mohammad2024-07-102024-07-102019-06-010017-095Xhttps://hdl.handle.net/11452/43122Given 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.eninfo:eu-repo/semantics/closedAccessArithmetic progressionsGeometric progressionsElliptic curveEdwards curveHuff curveRational sequenceRational pointScience & technologyPhysical sciencesMathematics, appliedMathematicsArticle0004689635000045364541