Es imposible descomponer un cubo en dos cubos

The objective of this work is to study the proof of Fermat’s last theorem. We study some trivial cases of Fermat’s last theorem, Sophie Germain’s theorem, which established the first case of Fermat’s theorem, and we also study the local and modular Fermat problem. Finally, we will focus on the proof of Fermat’s last theorem by using elliptic curves, modular forms and the Shimura-Taniyama conjecture. To study all these problems, we have used differents techniques of algebraic number theory, elliptic curves, modular functions, L-functions and Galois representations.Universidad de Sevilla. Grado en Matemática