We appoint that 𝑦 2= 𝑥3±𝐴𝑥 are elliptic curves. As the change of compositions of 𝐴, the
range of rank became varied. We shall calculate the ranks of various elliptic curves …

We establish upper bounds for the number of primitive integer solutions to inequalities of the
shape 0<| F (x, y)| ≤ h 0<| F (x, y)|≤ h, where F (x, y)=(α x+ β y)^ r-(γ x+ δ y)^ r ∈ Z x, y F (x …

This Issues Column! This issue's Open Problem Column is by PG Walsh and is Integral
Points on Elliptic Curves: A Journey into Speculative Number Theory. Request for Columns …

The subject of elliptic curves is as old and rich as mathematics itself, going back almost 2000
years to the work of Diophantus. Moreover, as a topic of study, it may be among the leaders …

The Thue-Siegel method is applied to derive an upper bound for the number of solutions to
Thue's equation $ F (x, y)= 1$ where $ F $ is a quartic diagonalizable form with negative …

In this short note, we identify an error made in an earlier paper [Math. Comp. 68 (1999), no.
225, pp. 385–388] on simultaneous Pell equations, provide a revised statement of the main …

A SPECIAL FAMILY OF BINARY FORMS, THEIR INVARIANT THEORY, AND RELATED
COMPUTATIONS. by CHRISTOPHE DETHIER A DISSERTATION Present Page 1 A SPECIAL …

Numerous papers have studied the problem of determining upper bounds for the number of
integer points on elliptic curves of the form y 2= x 3− mx, and quartic curves of the form X 2 …