Maleeha Khawaja, Samir Siksek
Published 2024-01-06Version 1
Wiles' proof of Fermat's last theorem initiated a powerful new approach towards the resolution of certain Diophantine equations over $\mathbb{Q}$. Numerous novel obstacles arise when extending this approach to the resolution of Diophantine equations over totally real number fields. We give an extensive overview of these obstacles as well as providing a survey of existing methods and results in this area.
Diophantine equations of the form $Y^n=f(X)$ over function fields
On Modular Approach to Diophantine Equation $x^4-y^4=nz^p$ over Number Fields
On certain diophantine equations related to triangular and tetrahedral numbers
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