50 citations · 131 across the 25 of their papers we have counts for
25 papers
Hilbert's Tenth Problem and Mazur's Conjectures in Complementary Subrings of Number Fields
Kirsten Eisentraeger, Graham Everest, Alexandra Shlapentokh
We show that Hilbert's Tenth Problem is undecidable for complementary subrings of number fields and that the p-adic and archimedean ring versions of Mazur's conjectures do not hold…
The Repulsion Motif in Diophantine Equations
Graham Everest, Thomas Ward
Problems related to the existence of integral and rational points on cubic curves date back at least to Diophantus. A significant step in the modern theory of these equations was m…
The Uniform Primality Conjecture for the Twisted Fermat Cubic
Graham Everest, Ouamporn Phuksuwan, Shaun Stevens
On the twisted Fermat cubic, an elliptic divisibility sequence arises as the sequence of denominators of the multiples of a single rational point. We prove that the number of prime…
Dual Rectangles
Graham Everest, Jonny Griffiths
This article has been written for an educational magazine whose target audience consists of students and teachers of mathematics in universities, colleges and schools. It concerns…
A Generalization of Siegel's Theorem and Hall's Conjecture
Graham Everest, Valery Mahe
Consider an elliptic curve, defined over the rational numbers, and embedded in projective space. The rational points on the curve are viewed as integer vectors with coprime coordin…
The uniform primality conjecture for elliptic curves
Graham Everest, Patrick Ingram, Valery Mahe +1
An elliptic divisibility sequence, generated by a point in the image of a rational isogeny, is shown to possess a uniformly bounded number of prime terms. This result applies over…