M. Sadek

activity

20102023

most citedMinimal Genus One Curves

5 citations · 16 across the 33 of their papers we have counts for

collaborators

Showing 2016Show all

5 papers · 1 filter

math.NT2016

On rational triangles via algebraic curves

Mohammad Sadek, Farida shahata

A rational triangle is a triangle with rational side lengths. We consider three different families of rational triangles having a fixed side and whose vertices are rational points…

math.NT2016

High rank quadratic twists of pairs of elliptic curves

Mohammad Sadek, Mohamed Alaa

Given a pair of elliptic curves $E_{1}$ and $E_{2}$ over the rational field $Q$ whose $j$ -invariants are not simultaneously 0 or 1728, Kuwata and Wang proved the existence of i…

math.NT2016

On dependence of rational points on elliptic curves

Mohammad Sadek

Let $E$ be an elliptic curve defined over $Q$ . Let $Γ$ be a subgroup of $E (Q)$ and $P \in E (Q)$ . In [1], it was proved that if $E$ has no nontrivial rational…

math.NT2016★ 1 cited

On sequences of consecutive squares on elliptic curves

Mohamed Kamel, Mohammad Sadek

Let $C$ be an elliptic curve defined over $Q$ by the equation $y^{2} = x^{3} + A x + B$ where $A, B \in Q$ . A sequence of rational points $(x_i,y_i)\in C(\mathbb Q),\,i=1,2,\ldot…

math.NT2016

On geometric progressions on hyperelliptic curves

Mohamed Alaa, Mohammad Sadek

Let $C$ be a hyperelliptic curve over $Q$ described by $y^{2} = a_{0} x^{n} + a_{1} x^{n - 1} + \dots + a_{n}$ , $a_{i} \in Q$ . The points $P_{i} = (x_{i}, y_{i}) \in C (Q)$ , $i=1,2,...,…