| dc.contributor |
Dieulefait, L. V. (Luis Victor) |
|
| dc.creator |
Madrid Gómez, Jaime |
|
| dc.date |
2018-05-25T08:37:38Z |
|
| dc.date |
2018-05-25T08:37:38Z |
|
| dc.date |
2018-01-19 |
|
| dc.date.accessioned |
2024-12-16T10:26:27Z |
|
| dc.date.available |
2024-12-16T10:26:27Z |
|
| dc.identifier |
http://hdl.handle.net/2445/122571 |
|
| dc.identifier.uri |
http://fima-docencia.ub.edu:8080/xmlui/handle/123456789/21103 |
|
| dc.description |
Treballs Finals de Grau de Matemàtiques, Facultat de Matemàtiques, Universitat de Barcelona, Any: 2018, Director: Luis Victor Dieulefait |
|
| dc.description |
[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. |
|
| dc.format |
45 p. |
|
| dc.format |
application/pdf |
|
| dc.language |
spa |
|
| dc.rights |
cc-by-nc-nd (c) Jaime Madrid Gómez, 2018 |
|
| dc.rights |
http://creativecommons.org/licenses/by-nc-nd/3.0/es |
|
| dc.rights |
info:eu-repo/semantics/openAccess |
|
| dc.source |
Treballs Finals de Grau (TFG) - Matemàtiques |
|
| dc.subject |
Nombres naturals |
|
| dc.subject |
Teoria de nombres |
|
| dc.subject |
Cub |
|
| dc.subject |
Treballs de fi de grau |
|
| dc.subject |
Natural numbers |
|
| dc.subject |
Number theory |
|
| dc.subject |
Cube |
|
| dc.subject |
Bachelor's theses |
|
| dc.title |
Teorema de Waring |
|
| dc.type |
info:eu-repo/semantics/bachelorThesis |
|