Revisiting the Fermat-type equation x13 + y13 = 3z7
Abstract
We solve the Fermat-type equation \[ x13 + y13 = 3 z7, (x,y,z) = 1 \] combining a unit sieve, the multi-Frey modular method, level raising, computations of systems of eigenvalues modulo 7 over a totally real field, and results for reducibility of certain Galois representations.
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