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 …

Let $ C: y^ 2= ax^ 4+ bx^ 2+ c $, be an elliptic curve defined over $\mathbb {Q} $. A set of
rational points $(x_i, y_i)\in C (\mathbb {Q}) $, $ i= 1, 2,\cdots, $ is said to be a sequence of …

We study the arithmetic (geometric) progressions in the x-coordinates of quadratic points on
smooth planar curves defined over a number field k. Unless the curve is hyperelliptic, we …

One is the creation of all the great people in his life. To Prof. Nabil L. Youssef, for standing
beside me from the very beginning, helping me through the complicated procedure of …