Guitart Morales, XavierArnalot Farràs, Joan2020-09-172020-09-172020-07-02https://hdl.handle.net/2445/170688Treballs Finals de Grau de Matemàtiques, Facultat de Matemàtiques, Universitat de Barcelona, Any: 2020, Director: Xavier Guitart Morales,[en] Hasse-Minkowski theorem states that a quadratic form has a non-trivial solution in $\mathbb{Q}$ if and only if there is a non-trivial solution in every completition. In this work we will study these completitions, their properties and their solutions in polynomials, the proof of the theorem and some applications and counterexamples in other polynomials than quadratic forms.54 p.application/pdfcatcc-by-nc-nd (c) Joan Arnalot Farràs, 2020http://creativecommons.org/licenses/by-nc-nd/3.0/es/Formes quadràtiquesTreballs de fi de grauNombres p-àdicsAnàlisi diofànticaQuadratic formsBachelor's thesesp-adic numbersDiophantine analysisinfo:eu-repo/semantics/bachelorThesisinfo:eu-repo/semantics/openAccess