Zarzuela, SantiagoMaristany Sala, Pau2019-01-172019-01-172018-06-27https://hdl.handle.net/2445/127363Treballs Finals de Grau de Matemàtiques, Facultat de Matemàtiques, Universitat de Barcelona, Any: 2018, Director: Santiago Zarzuela[en] Let $a_{1},..., a_{n}$ be positive integers, find the largest natural number that is not representable as a non-negative combination of $a_{1},..., a_{n}$. This problem is called Frobenius Problem. The project consists on a exposition of some of the most important results about this problem. We will study it using numerical semigroups and Hilbert series. We will prove that Frobenius Problem is $\mathcal{NP}$-hard and also that there is no polynomial formula for the general case.61 p.application/pdfcatcc-by-nc-nd (c) Pau Maristany Sala, 2018http://creativecommons.org/licenses/by-nc-nd/3.0/es/Nombres naturalsTreballs de fi de grauAnàlisi diofànticaSemigrupsÀlgebra commutativaNatural numbersBachelor's thesesDiophantine analysisSemigroupsCommutative algebrainfo:eu-repo/semantics/bachelorThesisinfo:eu-repo/semantics/openAccess