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STNB2025( 38a edició)

On the Fermat equation x13+y13=3z7

Ponents

Nuno Freitas

Resum

The modular method is a fantastic tool to solve families of Diophantine equations with a varying exponent, but it often fails for small values of the exponent. For example, the Fermat-type equation x13+y13=3zp has been solved for all p7. In this talk we will discuss how a combination of a unit sieve, modular method, level raising, computations of systems of eigenvalues modulo 7 and results for reducibility of certain Galois representations, allows to solve the missing case p=7.

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