13 papers · 1 filter
Construction of Polynomials with prescribed divisibility conditions on the critical orbit
Mohammad Sadek, Mohamed Wafik
We consider the family of polynomials over the rational field $\Q$. Fixing integers , we show that the density of primes that can appear as primitive…
Divisibility by 2 on quartic models of elliptic curves and rational Diophantine -quintuples
Mohammad Sadek, Tuğba Yesin
Let be a smooth genus one curve described by a quartic polynomial equation over the rational field with . We give an explicit criterion for the d…
Families of polynomials of every degree with no rational preperiodic points
Mohammad Sadek
Let be a number field. Given a polynomial of degree , it is conjectured that the number of preperiodic points of is bounded by a uniform bound that d…
Rational Points in Geometric Progression on the Unit Circle
Gamze Savaş Çelik, Mohammad Sadek, Gökhan Soydan
A sequence of rational points on an algebraic planar curve is said to form an -geometric progression sequence if either the abscissae or the ordinates of these points form a geo…
Strong rational Diophantine D(q)-triples
Andrej Dujella, Matteo Paganin, Mohammad Sadek
We show that for infinitely many square-free integers q there exist infinitely many triples of rational numbers {a, b, c} such that a^2 + q, b^2 + q, c^2 + q, ab + q, ac + q and bc…
Rational sequences on different models of elliptic curves
Gamze Savaş ÇELİK, Mohammad Sadek, Gökhan Soydan
Given a set of elements in a number field , we discuss the existence of planar algebraic curves over which possess rational points whose -coordinates are exactly the…