Browsing by Author "Sadek, Mohammad"

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    Rational points in geometric progression on the unit circle
    (Kossuth Lajos Tudomanyegyetem, 2021-01-01) Çelik, Gamze Savaş; Sadek, Mohammad; Soydan, Gökhan; Çelik, Gamze Savaş; SOYDAN, GÖKHAN; Bursa Uludağ Üniversitesi/Fen-Edebiyat Fakültesi/Matematik Bölümü; 0000-0002-6321-4132; EPC-6610-2022; GEK-9891-2022
    A sequence of rational points on an algebraic planar curve is said to form an r-geometric progression sequence if either the abscissae or the ordinates of these points form a geometric progression sequence with ratio r. In this work, we prove the existence of infinitely many rational numbers r such that for each r there exist infinitely many r-geometric progression sequences on the unit circle x(2) + y(2) = 1 of length at least 3.
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    Rational sequences on different models of elliptic curves
    (Croatian Mathematical Soc, 2019-06-01) Sadek, Mohammad; Soydan, Gökhan; SOYDAN, GÖKHAN; Çelik, Gamze Savaş; Bursa Uludağ Üniversitesi/Fen Edebiyat Fakültesi/Matematik Anabilim Dalı.; 0000-0002-6321-4132; M-9459-2017
    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.