REVISITING THE FERMAT-TYPE EQUATION x^{13} + y^{13} = 3 z^{7}
Résumé
We solve the Fermat-type equation
x 13 + y 13 = 3z 7 , gcd(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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