Highly Influenced

@inproceedings{Dahmen2009ARM, title={A Refined Modular Approach to the Diophantine}, author={Sander R. Dahmen}, year={2009} }

- Published 2009

Let n be a positive integer and consider the Diophantine equation of generalized Fermat type x2 + y2n = z3 in nonzero coprime integer unknowns x, y, z. Using methods of modular forms and Galois representations for approaching Diophantine equations, we show that for n ∈ {5, 31} there are no solutions to this equation. Combining this with previously known results, this allows a complete description of all solutions to the Diophantine equation above for n ≤ 107. Finally, we show that there are… CONTINUE READING