Treballs Finals de Grau de Matemàtiques, Facultat de Matemàtiques, Universitat de Barcelona, Any: 2016, Director: Artur Travesa i Grau
Since 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.