5 papers · 1 filter
Arithmetic progressions in polynomial orbits
Mohammad Sadek, Mohamed Wafik, Tuğba Yesin
Let be a polynomial with integer coefficients whose degree is at least 2. We consider the problem of covering the orbit , whe…
A Dynamical Analogue of a Question of Fermat
Mohammad Sadek, Tuğba Yesin
Given a quadratic polynomial with rational coefficients, we investigate the existence of consecutive squares in the orbit of a rational point under the iteration of the polynomial.…
Rational points on quadratic elliptic surfaces
Mohammad Sadek
We consider elliptic surfaces whose coefficients are degree polynomials in a variable . It was recently shown that for infinitely many rational values of the resulting e…
High rank quadratic twists of pairs of elliptic curves
Mohammad Sadek, Mohamed Alaa
Given a pair of elliptic curves and over the rational field whose -invariants are not simultaneously 0 or 1728, Kuwata and Wang proved the existence of i…
On the Diophantine equation cy^l=(x^p-1)/(x-1)
Mohammad Sadek
Let p, c be distinct odd primes, and l \ge 2 an integer. We find sufficient conditions for the Diophantine equation cy^l=(x^p-1)/(x-1) not to have integer solutions