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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…