Barcelona Fall Workshop on Number Theory
On some Fermat-type equations
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Resumen
The modular method for Diophantine equations breaks into the
following main steps: construction of a Frey curve, modularity,
irreducibility, level lowering and discarding newforms. Due to
historical reasons it is considered that the modularity step is the
hardest, but this may be misleading. In this talk I will discuss
examples where the step "discarding newforms" is the major
obstruction and its relation with the Frey-Mazur conjecture.
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