# metadata.dc.description[].value
Treballs Finals de Grau de Matemàtiques, Facultat de Matemàtiques, Universitat de Barcelona, Any: 2018, Director: Luis Victor Dieulefait

# metadata.dc.description.abstract[].value
[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.

# metadata.dc.rights[].value
cc-by-nc-nd (c) Jaime Madrid Gómez, 2018

# metadata.dc.source[].value
Treballs Finals de Grau (TFG) - Matemàtiques