Barcelona Fall Workshop on Number Theory
On some Fermat-type equations
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Abstract
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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