1 citations · 1 across the 7 of their papers we have counts for
10 papers
On representing coordinates of points on elliptic curves by quadratic forms
Andrew Bremner, Maciej Ulas
Given an elliptic quartic of type representing an elliptic curve of positive rank over $\Q$, we investigate the question of when the -coordinate can be represented by…
Squares in arithmetic progression over cubic fields
Andrew Bremner, Samir Siksek
Euler showed that there can be no more than three integer squares in arithmetic progression. In quadratic number fields, Xarles has shown that there can be arithmetic progressions…
Points at rational distances from the vertices of certain geometric objects
Andrew Bremner, Maciej Ulas
We consider various problems related to finding points in $\Q^{2}$ and in $\Q^{3}$ which lie at rational distance from the vertices of some specified geometric object, for example,…
Constructions of diagonal quartic and sextic surfaces with infinitely many rational points
Andrew Bremner, Ajai Choudhry, Maciej Ulas
In this note we construct several infinite families of diagonal quartic surfaces \begin{equation*} ax^4+by^4+cz^4+dw^4=0, \end{equation*} where with in…
On certain diophantine equations of diagonal type
Andrew Bremner, Maciej Ulas
In this note we consider Diophantine equations of the form \begin{equation*} a(x^p-y^q) = b(z^r-w^s), \quad \mbox{where}\quad \frac{1}{p}+\frac{1}{q}+\frac{1}{r}+\frac{1}{s}=1, \en…
Some observations concerning reducibility of quadrinomials
Andrew Bremner, Maciej Ulas
In a recent paper \cite{Jan}, Jankauskas proved some interesting results concerning the reducibility of quadrinomials of the form , where . He a…