Travesa i Grau, ArturCaelles i Vidal, Marc2016-04-212016-04-212016-01-18https://hdl.handle.net/2445/97731Treballs Finals de Grau de Matemàtiques, Facultat de Matemàtiques, Universitat de Barcelona, Any: 2016, Director: Artur Travesa i GrauSince every finite extension over the field $\mathbb{Q}_p$ of $p$-adic numbers is solvable, any degree 5 polynomial can be solved by radicals over the field of $p$-adic numbers. Using Panayi's algorithm we describe a method for expressing any root of an irreducible quintic over $\mathbb{Q}_p$ as a $\mathbb{Q}_p$-linear combination of radical expressions over the rationals.57 p.application/pdfcatcc-by-nc-nd (c) Marc Caelles i Vidal, 2016http://creativecommons.org/licenses/by-nc-nd/3.0/esNombres p-àdicsTreballs de fi de grauCamps p-àdicsPolinomisEquacionsAlgorismesp-adic numbersBachelor's thesesp-adic fieldsPolynomialsEquationsAlgorithmsinfo:eu-repo/semantics/bachelorThesisinfo:eu-repo/semantics/openAccess