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http://hdl.handle.net/2445/122571
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DC Field | Value | Language |
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dc.contributor.advisor | Dieulefait, L. V. (Luis Victor) | - |
dc.contributor.author | Madrid Gómez, Jaime | - |
dc.date.accessioned | 2018-05-25T08:37:38Z | - |
dc.date.available | 2018-05-25T08:37:38Z | - |
dc.date.issued | 2018-01-19 | - |
dc.identifier.uri | http://hdl.handle.net/2445/122571 | - |
dc.description | Treballs Finals de Grau de Matemàtiques, Facultat de Matemàtiques, Universitat de Barcelona, Any: 2018, Director: Luis Victor Dieulefait | ca |
dc.description.abstract | [en] In number theory, Waring’s problem (1770) asks whether for each natural number k exists an associated positive integer $s(k)$ such that every natural number is the sum of at most s natural numbers to the power of $k$. The statement was proved by Hilbert in 1909. We present an overview of Hilbert-Waring theorem. First, we introduce the modern notation and find several lower and upper bounds using elementary methods. Next, we offer a proof of the theorem based on Schnirelmann’s density. Finally, we summarize the current state of the problem. | ca |
dc.format.extent | 45 p. | - |
dc.format.mimetype | application/pdf | - |
dc.language.iso | spa | ca |
dc.rights | cc-by-nc-nd (c) Jaime Madrid Gómez, 2018 | - |
dc.rights.uri | http://creativecommons.org/licenses/by-nc-nd/3.0/es | - |
dc.source | Treballs Finals de Grau (TFG) - Matemàtiques | - |
dc.subject.classification | Nombres naturals | ca |
dc.subject.classification | Treballs de fi de grau | - |
dc.subject.classification | Teoria de nombres | ca |
dc.subject.classification | Cub | ca |
dc.subject.other | Natural numbers | en |
dc.subject.other | Bachelor's theses | - |
dc.subject.other | Number theory | en |
dc.subject.other | Cube | en |
dc.title | Teorema de Waring | ca |
dc.type | info:eu-repo/semantics/bachelorThesis | ca |
dc.rights.accessRights | info:eu-repo/semantics/openAccess | ca |
Appears in Collections: | Treballs Finals de Grau (TFG) - Matemàtiques |
Files in This Item:
File | Description | Size | Format | |
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memoria.pdf | Memòria | 353.52 kB | Adobe PDF | View/Open |
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