A Refined Modular Approach to the Diophantine

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

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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 .
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