Cazorla García, Pedro-José 2025-11-13T10:05:34Z 2025-11-13T10:05:34Z 2025-11-30 0035-6298 http://hdl.handle.net/11531/107185 Artículos en revistas . Generalised Pythagorean triples are integer tuples (x, y, z) satisfying the equation Ea,b,c : ax2 + by2 + cz2 = 0. A significant amount of research has been devoted towards understanding generalised Pythagorean triples and, in particular, we can now determine whether Ea,b,c has solutions and find them in a computationally effective manner. In this paper, we consider an extension of generalised Pythagorean triples to number fields K. In particular, we survey and extend the existing results over Q for determining if Ea,b,c has solutions over number fields and if so, to find and parameterise them, as well as to find a minimal solution. Throughout the text, we incorporate numerous examples to make our results accessible to all researchers interested in the topic of generalised Pythagorean triples. application/pdf en-GB Revista: Rivista di Matematica della Universita di Parma, Periodo: 1, Volumen: on line first, Número: , Página inicial: 1, Página final: 22 On generalised Pythagorean triples over number fields info:eu-repo/semantics/article info:eu-repo/semantics/publishedVersion 5 años de embargo info:eu-repo/semantics/restrictedAccess . Pythagorean triples, Diophantine equations, number fields, LLL algorithm, computational number theory.