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Revisiting the Fermat-type equation $x^{13} + y^{13} = 3z^7$

Published 15 Oct 2025 in math.NT | (2510.13773v1)

Abstract: We solve the Fermat-type equation [ x{13} + y{13} = 3 z7, \qquad \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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