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memoria.pdf (353.52 KB)

Document type

Bachelor thesis

Publication date

2018-01-19

Publication license

cc-by-nc-nd (c) Jaime Madrid Gómez, 2018
Please use this identifier to cite or link to this item: https://hdl.handle.net/2445/122571

Teorema de Waring

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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.

Description

Treballs Finals de Grau de Matemàtiques, Facultat de Matemàtiques, Universitat de Barcelona, Any: 2018, Director: Luis Victor Dieulefait

Subject

Nombres naturals, Treballs de fi de grau, Teoria de nombres, Cub

Subject (English)

Natural numbers, Bachelor's theses, Number theory, Cube

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Treballs Finals de Grau (TFG) - Matemàtiques

Citation

MADRID GÓMEZ, Jaime. Teorema de Waring. [consulted: 12 of August of 2026]. Available at: https://hdl.handle.net/2445/122571

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