Modular congruences, Q-curves, and the diophantine equation x^4 + y^4 = z^p

2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/67266We prove two results concerning the generalized Fermat equation $x^4+y^4=z^p$. In particular we prove that the First Case is true if $p \neq 7$.Number TheoryAlgebraic Geometry11D41; 11F11Modular congruences, Q-curves, and the diophantine equation x^4 + y^4 = z^ptext